27


interaction between industry catch and the population growth rate,

equation (12) can be rewritten as

 X = f(X, m) Vx (13)


This form of equation (13) can be interpreted to mean that the sus-

tainable yield produced by any given stock and fixed mesh size is

reduced by an amount precisely equal to industry catch.

 In dealing with the individual firm, Smith (1969) chooses to define

behavior in terms of the firm's long-run cost function. It should be

emphasized that the firm's production function is implicity in the cost

function. The general form of the cost function is

 c = 5(x, X, m, V) + ( (14)


where T is defined to be the firm's opportunity cost. Partial effects

are hypothesized to be, c = > 0, c2 0, c3 > 0 and
 -1 a-x > 01c X = am
 c4 E > 0. Of interest here is the fact that stock externality
 4 aV -
 effects, c2, and productive interdependency effects, c4, can be equal to

 zero.

 Industry revenue (R) is defined to be a function of industry catch

 and mesh size. Mathematically, this relationship is expressed by

 R = R(Vx, m) (15)

 From this relationship the price of output received by individual firms

 in the industry can be shown to be


 P(m) R(Vx, m) (16)
 P(m) = Vx