Q2 Z2,(Q2) Z2(Q2) - Institute for Water Resources - U.S. Army

2. Two Markets Model.
subject --co
and
Suppose that two markets are available at each end of the river,
but that the second market can be reached only by water, while the first
one can be reached by the three modes. The choice problem is considerably
complicated since the number of binary choices, and partial boundaries is
augmented by three. However, each of these new boundaries can be
derived as easily as were the others.
If the two-market prices are different, they must be taken into
account in the shipping decision. For. doing so, it is necessary to consider
the net income indifference locus rather than the transportation cost
indifference locus.
For the competition between market A and market B through truck-
water transportation, the boundary is defined by: ,
(5) - Ct 1(X0 - Xi ) 2 + Y) - - CwaXi Lwa =
P b - C t
'Co - X 1 -
X - X =
CwN
(C 2 -C 2 ) i
t wa
ewbfrOl
2 o (c - c )
X 0' X 1 - 0.
.t wb
1
■
t • • wb 3 2 wb
Where Pa and Pb are the commodity market prices at A and B respectively, X 3
is the trans-shipment point on the river
is the distance between A and B, X
2
Awl the grain is shipped to B, and Cwa ,and Cwb are the barge rates toA and
B respectively, and •lisla and Lwb are the fixed costs to A and B respectively,
The two restrictions guarantee that optimal trans-shipment points are selected.
The second one can be derived as the first one was in Chapter IV.
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