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

CHAPTER I
The Firm's Transport Demand in Perfect Competition.
Consider a firm that operates under conditions of perfect
competition. It is located at A and sells all of its output of a single
homogeneous product in a market located at B. The firm purchases all of
its inputs locally so that the only transport it requires is for shipping
its product to market. In order to introduce the two problems of mode
choice and quantity the firm will ship in the simplest possible manner,
two modes with radically different characterisitcs will be assumed. One
of them is very expensive but very fast: it will be treated as instanta7
neous in the theoretical model. The other mode is very slow but very
cheap: the firm's cost function is given. The price of its product in
the market (P), the number of days required to ship the product to the
market by the slow mode (a), the interest rate per day (i) and the per
unit transport cost by the fast mode (g) are also given.
the form:
Suppose the firm's total cost (of production) function is of
(1) C = Z n , where Z is output per day and n > 1.
The firm's total cost of producing and shipping by the fast mode will then be:
(2) C 1 = Z n + gZ.
Total cost of producing and shipping by the slow mode is:
(3) C 2 = Cl + i) aZn , where the term (1 1. i) aZn represents the interest
charge on the money the firm must tie up in production cost when it ships
by the slow mode.
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