The origin (j = 0) is included as a destination because one
alternative is to sell the commodity at the origin. The
(derived) demand equation for transport for commodity i to
destination j is obtained by taking the negative of the
derivative of PROFIT with respect to ti,j:
(5) QTRANSi,j = -fRATE(i,j), (RATE, SC, DC, CHVAL).
Of course, QTRANS must be non-negative, and the constraint
that the amount shipped cannot exceed supply must hold. As
is the case for many agricultural activities, it is probably
more appropriate to invert the demand equation, making RATE
a function of quantity:
(6) RATEij = f-1 (QTRANS, SC, DC, CHVAL)
where f-I is the inverse of f with respect to RATEij.
If any of the variables in the profit equation differ across
commodities, the demand for transport will also vary across
commodities. If transportation services are homogeneous and
if those with differing demand characteristics can be segrega-
ted, then price discrimination might occur. On the other
hand, if transportation services are nonhomogeneous, then the
differences in demand may result in the purchase of different
levels and mixtures of service characteristics. The latter is
particularly likely if the market structure precludes effective
segregation of demand groups and/or pricing discipline among
the vendors, and if the barriers to entry are low.
The supply of transport services can be derived in similar
fashion. The expected profits of carriers are the discounted
present values of their net earnings from their next trips and
from all following trips. Their profit equations include freight
rates (RATE), operating costs (OPCST), costs related to
queuing for their next shipments (QU), and expected search
costs at destinations and the probability of not obtaining an
outbound load (EREV):
(7) PROFITcar = g(RATE, OPSCT, QU, EREV)