43


 P r/ i = .., n (30)
 1 r X.

 dP
From equation (24) it can be shown that (P + dC C) is always less than

P. This taken in conjunction with equations (23a) and (23b) can be

used to show that the input levels satisfying equation (30), say X ,

must be such that X' > X. for all i. Thus, the obvious result that

input levels under the management strategy of marginal cost pricing are

greater than those corresponding to profit maximization is obtained.

A Multi-Sector Fishery

 The term fishery is somewhat synonymous with the traditional

definition of an industry. A sector is defined in this study to be a

sub-industry defined in terms of geographical location. Thus, if a

large fishery is composed of several states or distinct geographic

regions, under the above definition, each state or region can be con-

strued as a single sector.

 To begin the analysis of a multi-sector fishery, assume there are

 N sectors or regions, each facing a demand function defined by

 P = P.(C1, ..., CN) i = 1, ... N (31)

 th
 where P. is the price received by producers in the i region and the C.

 correspond to the outputs of the N regions. It should be emphasized

 here that the C. are assumed to be the same product. The subscript

 refers to regions rather than commodities. This form of the demand

 equation will be discussed later. The demand equations given in equa-

 tion (31) are assumed to be such that