the resource stock in any given time period can then be given by

 St = S + X(C_1 Ct) (48)


where St is the stock size in time t, Ct is sustainable yield produced
by the resource stock in time t, Ct is the corresponding catch and X is
a constant of proportionality. Thus, equation (48) states that the

stock size in time t is equal to the stock size in the preceding time

period plus a proportion of the difference between sustainable yield and
catch in time t-l. While only Ct_1 is observable, equation (48) serves
to suggest that the resource stock variable is at least to a certain
degree, autocorrelated. Thus, the omission of the resource stock vari-
able is expected to generate some systematic variation in the distur-

bances of the catch equation which can be approximated by an
autoregressive process. In particular then, the stochastic process
corresponding to the ith region's catch equation is assumed to take the
general form

 A'(S) = A' + U (49)
 it 1 it


where A! is constant and the disturbance term, Uit, is postulated to be
characterized by a pth order autoregressive process. On substitution of
equation (49) into equation (47) the ith state's catch equation can be
expressed as


 cit = A + Bivt + li xlit + 2ix2it + Uit (50)


 where Uit= PliUt- + p2i Ui,t-2 + + Ppi Ut-P + eit and eit is