where Cit represents combined catch of red snapper and grouper, A(S)it

is a stochastic process generated by the resource stock, Eit is total

effort and .i is a constant. The aggregation of red snapper and

grouper into a single catch variable is an unfortunate result of limited

data. While separate catch series are available, input data are not

disaggregated to permit an analysis of the allocation of these inputs

between species.

 The form of the catch equation, as with the fishing power equation,

was chosen in part due to the ability of such a function to capture a

non-linear relationship between catch and effort while retaining an

intrinsic linear form for estimation purposes. The form chosen does,

however, lend itself to an approximate test of an interesting hypothesis.

The notion of returns to scale is a somewhat misleading notion with

respect to fisheries production due to the dynamic nature of the

resource stock. It has been used, however, in fishery production

literature (Schaefer, 1957; Scott, 1955). More precisely, the non-

equilibrium catch equations utilized in stock production models gener-

ally assume constant returns to scale as exhibited by the ith state's

catch equation. Acceptance that the stochastic process, A(S)it, in

equation (45) adequately accounts for the effects of the resource stock

on catch allows the utilization of the pi parameter to conduct an ap-

proximate test of the "constant returns" assumption of the stock produc-

tion models of Schaefer (1957) and Pella and Tomlinson (1969).



 3The specification of the stochastic nature of A(S)it will be
 discussed more fully in the latter portion of this section.