47


 aP
 MR. MC. = Ck C(38)
 S 1 kfi aC k

 f.
where MCi has replaces the expression r / it can be seen that the
 1

sign of the difference between MR. and MC. is given by the sign of
 P 9P k
 -C Ck. From equation (31a), < 0 for all i, k and Y is
 ki aCi k aC k

 strictly positive. Therefore, the sign of the right-hand side of equa-

 tion (38) must be greater than zero, implying that MRi is greater than

 MC.. It should be noted here that a sufficient condition for MRi = MCi

 aP
 is that 0, i k. In this case, independent maximization of
 aC

 regional profits is equivalent to maximizing profit in all regions

 simultaneously.
 .th
 The implications of these results on input levels for the i

 region can be seen by examining Figure 9. The figure illustrates that

 equating MR. and MC. results in an output of Cli, which is greater than

 that produced, C2i, under the equilibrium conditions stated in equation
 aP
 (37). The distance OA-OB is equal to kC- C Taken in conjunction
 k=i i 1
 with the nature of the yield function (equations (23a) and (23b)), it

 can be concluded that inputs are at lower levels when cross-regional

 price effects are taken into account.

 As in the case of a single sector fishery, the question of produc-

 ing at the point where price is equated to marginal cost must be con-

 sidered in the multi-sector fishery. As with the single sector fishery,

 assume that the desired yield levels have been determined for each

 region. In that fixing yield levels results in fixing price, the

 profit maximization problem reduces to a cost minimization problem with