42


Substitution of P + P C into equation (27b) for X yields


 (P+ CdP C- r. i 1 n (28)



The expression in equation (28) states that in equilibrium, the marginal
 +th
revenue product of the thinput must be equated to its price, or

equivalently, its marginal cost. Equation (28) can be rewritten in an

alternative and perhaps more illuminating fashion as


 (P + C) r/i= ,..., n (29)
 dC 1 X."

 af / f
 From equation (29) it is readily seen that r / = r. / for all
 i e ji
 i and j. Now, in equilibrium, ri / is precisely equal to the

 marginal cost of output. Hence, equation (29) states the well-known

 result that, in equilibrium, marginal cost equals marginal revenue.

 Equation (29) provides a convenient way of examining some possible

 consequences of various management goals. One can consider the implica-

 tions with respect to input usage levels under various management goals.

 In this case, the industry is treated as a single firm and the manage-

 ment goal is defined to be profit maximization. The relevant equations

 to be solved in this case are given by equations (27a-27c). Assume

 that the input levels resulting from this solution are denoted by Xi,

 i = 1, ..., n. Consider now the relationship between these input levels

 and those that would result if the fishery was managed at price equals

 marginal cost. Under this regime, the equilibrium equations analogous

 to equation (29) would be