Substituting Equations (10) and (11) into Equa- 

 tion (16): 



n = p\aKS«-^-I K - H K - 8^. (17) 



Taking the first and second derivatives of Equa- 

 tion (17) with respect to the soak time: 



dir _ (1 - (3) paK _SK> Q 

 dS SP D < 



d 2 7T _((3 2 - p) paK 



dS'' 



S<l + /3> 



< 0. 



(18) 



(19) 



The profit-maximizing soak time can be deter- 

 mined by setting Equation (18) equal to zero and 

 solving for S (Figure 5): 



>•-£ 



- j8) paP \ 

 8 J 



(20) 



X K + "k 



Estimated life span of a trap: 1.5 seasons or 12 



mo 

 8 = depreciated value of a trap forD days use (1 



mo) 

 8 = 630 

 p = 38.30 

 D = 30 

 a = 2.94 

 j8 = 0.90 

 S„ = 6.52 (as estimated by Equation (20)). 



The theoretically profit-maximizing soak time 

 compares favorably with the average soak time of 

 6-7 days in 1962 (October-December) observed by 

 Robinson and Dimitriou in the commercial 

 fishery. This favorable comparison should be 

 interpreted with reservations. First, Equation (1) 

 was estimated from a small sample (25 observa- 

 tions). Second, the model is sensitive to trap costs 

 and the method of calculating these costs is rather 

 crude. The life span of traps varies significantly. 

 Furthermore, maintenance costs involve remov- 

 ing underwater growth (traps fish better when 

 they are clean) and onshore storage costs that vary 

 considerably at different locations. 



Influence of Relative Abundance on 

 Soak Time and Catch per Trap Day 



The catch per trap day may not reflect declining 

 relative abundance (decreasing a in the model). As 

 the exploitable stock declines so will the profit- 

 maximizing soak time (Equation (20)). This re- 

 duces the number of traps each vessel can operate 

 (given a maximum number of hauls) but increases 

 the catch per trap day relative to what would have 

 prevailed with the originally longer soak time. 

 The net result is that as a declines the catch per 

 trap day will remain constant. This can be seen by 

 substituting Equation (20) into Equation (1). 



FIGURE 5. — Total revenue, total cost, and profit with respect to 

 the soak time, given combinations of soak time and number of 

 traps that always result in the maximum number of hauls. 



L_ 

 TD 



a 



a 



SI 



|l - fl) paD] y] 



The parameters prevailing in 1962 were: 



Purchase price of a trap: $6.00 



Maintenance cost of a trap over its life span: 



(0.25)(cost) = $1.50 

 Total cost of a trap: $7.50 



(1 - 0) P D 



(21) 



Equation (21) and Table 1 indicate that the 

 measured catch per trap day will not vary with 

 changes in the exploitable stock when the soak 

 time also adjusts to the exploitable stock. 



216 



