26


the externalities of production. Three different types of production

externalities are said to exist. Stock externalities are assumed to

represent shifts in the firm cost function due to changes in the stock

size. Crowding externalities result from direct interdependence of pro-

duction (fishing) activities. Finally, Smith (1968) considers mesh

externalities which correspond to both the economic and biological

effects of changing mesh size. It should be noted that in any given

fishery, some or all of these externalities may or may not exist.

 The general formulation of the model centers on the assumption of

V homogeneous vessels, each producing x units of output. Total industry

catch is thus equal to Vx. The sustainable yield function used is

defined in general function form to be f(X) where X corresponds to the

resource stock size. This function is assumed to possess the following

properties: f(X) = f(X) = 0 where X and X are the maximum and minimum

viable populations, respectively, f x0 = 0 for some X < X < X, an
 d2f
interior maximum growth rate (MSY) exists, and finally 2 < 0 ruling
 dx
out any inflection point in the sustainable yield function. As noted

previously, the most common specific form of f(X) is the quadratic form

which corresponds to a logistic growth law.

 To bring fishing activity into the model, Smith expresses f(X) X

 as

 X = f(X, m, Vx) (12)


where m = mesh size and other variables are defined as above. Equation

(12) thus states that sustainable yield, X, is a function of population

size, mesh size and total industry catch. It is further assumed that X

is an "inverted U" shape with f3 V < 0. By ruling out any type of