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

and the probability distribution d[x m) of market prices (Pm) .
Inventory cost per unit per day is q. Perfect competition
exists in all markets.
When goods had to be sold on arrival in the market, as
was assumed previously, the profit maximizing output was
A
determined by assuming that P would be the net discounted
..-T
price that would prevail (where P = ).
0:0°4
With inventory holding allowed, the shipper now has
the option of shipping his goods, having them arrive oL
days from the date of shipment, viewing the market price
at that time and deciding whether he wishes to sell or to
hold the goods in inventory, waiting for a more attractive
market price. Although tomorrow's price may be higher, this
must be weighed against the inventory cost and the extra
time cost.
The analysis becomes more complicated as the number of
days a good can be held in inventory increases. It also is
more complicated the greater the variance of tP3 . To
avoid such problems yet showing the point of the analysis,
we constrain the inventory holding period to one day. That
is, the shipper either sells his good in the market on the
ot th or the o.+1 St day. After the ot41 St day, the good
spoils so that it is unsellable. The price probability
distribution is symmetrical, tx -t) where k=1,2,3. The
mean price will be Y 1) 2 .
It is clear that if the market price is P 3 on the 04 th
day, the shipper will sell all goods on that day - for he
never can do better. If the price is P 2 on the oc. th day,
the shipper will also choose to sell all his goods on that
day. Without any a priori knowledge, the price he expects
to prevail on the oc.4.1 St day is Te = P 2 . Getting P 2 today
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