44


 aP.
 < 0 all i, j(31a)
 aC

 th
 Turning to the yield equations, let the i region's catch function

be defined by

 C = f (X, ..., Xni) (32)


where the X.. refer to the jth input used in the ith region. It is
 u'
further assumed that fi (Xi' ..., Xni) i = 1, ..., N satisfy the con-

ditions stated in equations (23a) and (23b). Finally, assume that the

cost equation for the ithregion is given by

 n
 Ki = z r.X.. i = 1, ..., N (33)
 j=l j J1

where the r. are fixed input prices assumed the same for all regions.

 The profit maximization problem for the entire fishery can be

 stated as

 N N
 MAX ~r = Pi(C1', ... CN) C. K. (34)
 i=l i=l

 s.t. Yi = f(Xli, ..., Xni) i = 1, ..., N


 Once again, using the method of lagrange multipliers, equation (34) can
 be restated in the form

 MAX L = E Pi(C1, ..., CN) Yi K. + [f (X., .,.
 i i i
 Xi) Ci ] (35)