46


 aP af.
 1R k#i C i k 1 aX Jji

 af
This equation can be used to show that in equilibrium, r / = r. /

aff
 Small i, j, and that these expressions are in turn equal to the
Xji

marginal cost of output. From equation (37), it can then be seen that

the single result of within region marginal cost equals within region

marginal revenue does not necessarily hold when the industry is composed

of several regions of whose profit is jointly maximized.

 The reason for this apparent divergence between each region's

marginal cost and revenue can be explained by examining the second term
 aP
on the left-hand side of equation (37), E k C This term is equal
 kfi 3Ci k
to the sum of the change in total revenues in the N 1 regions induced

by a change in the output of the ith region. From this, the non-equality

of within region marginal costs and within region marginal revenues makes

more sense. The equating of within region marginal revenues and mar-

gional costs fails to account for interregional price effects. When

maximization deals with all sectors simultaneously, these price effects

are "internalized," resulting in the expression in equation (37).

 Having seen that simultaneous maximization of profit in the above

 situation does not result in the traditional result in the equality of

 each region's marginal cost and marginal revenue, it is of interest to

 determine the sign of difference between these two terms. Knowledge of

 this sign will enable comparison of input levels obtained under the

 above procedure and those obtained by maximization of each region's

 profit independently of other regions. Rewriting equation (37) as