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

•
goods arrive (so that Q A+Q S goods can confront the market).
However, if the A goods are sold when they arrive in the
market place now and the S goods are sold when they arrive 01,
days from now, the instantaneous demand function concept is
lost.
").
One could perhaps assume that the demand period was
for a certain length of time and that the market equilibrium
is determined by the end of that period, but that instant-
aneously arriving goods are sold right now at the equilibrium
market price. In such a caseP=4 f(Q A -1-Q S ) = rg = a-b(Q 4Q )
A S
Revenues are attributed when the goods arrive at the market
place. Hence, if modal splits exist, one set of total
revenues is received immediately and the other set is
received in 0C. days.
The overall profit function reads (after proper
discounting);
(1) . 1.6 (.‘ ) 12(A f t ‘I‘S 1* 1/46Z S 4 ‘:4"
or
0.9,s na•
(2) . tc °AA" %CAP:- CZA j la`s
w‘A
The optimal amount of goods shipped by air is found by:
6% •
0-443 - al•QA CT • • trAs 4 QA) =
.
The optimal amount of goods shipped by sea is found by:
7?‘
(4) .
2.1)GtS
"IAA
Gtis
+ (■4;..YL 01;‘r(417-)
1.10S+ GIA) 2
57