41


aK
Sr.
aX.


i = 1, ..., n


 Given these assumptions on the technical relationship between catch,

inputs and product and input prices, the profit maximization problem or

equivalently the MEY problem can be stated in the form


 n
MAX 7 = P(C)C z r X.
 i=1


(26)


 s.t. C = f(X, ..., Xn)


Equation (26) can be seen to be a constrained maximization problem with
 9
the constraint being the yield equation. Utilizing the method of

lagrange multipliers, equation (26) can be restated by

 n
 MAX L = P(C)C z r. x X[C f(X1, .., X )] (27)
 i=l n


Differentiation of equation (27) yields the first order conditions


aL p + dP
 = + C-x = o
aC dC

L = -r + X 0
ax. ax.
 1 1


i = 1, ..., n


a = f(X .. X ) -C =0
ax 1 n


Examination of the first equation indicates that the lagrange multiplier,
 dP
X, is equal to P + -C C, which is precisely marginal revenue.


 9 s section draws upon Intri gator (1971
 This section draws upon Intrilligator (1971).


(25b)


(27a)


(27b)



(27c)