nations that always result in the maximum 

 number of possible hauls. 



L = 



(m)- 



aKS 



(1-/3) 



(11) 



Taking the first and second derivatives of Equa- 

 tion (11) with respect to the soak time: 



dL = (1 - j8) aK 



dS SO 



d 2 L __ (/3 2 - j8) aK 



dS'- 



S'i^> 



< 0. 



(12) 



(13) 



Equations (12) and (13) imply that, holding the 

 number of total hauls constant, the total catch 

 increases at a decreasing rate with respect to the 

 soak time (Figure 4). This is because a longer soak 

 time decreases the catch per trap day but increases 

 the number of traps that can be fished. 



The fisherman/entrepreneur is not interested in 

 maximizing the catch per trap day, the catch per 

 trap haul, or the total catch. He presumably wants 

 to maximize the net economic return (profit) from 

 fishing which is the difference between the total 

 revenue and total cost of his fishing activities. The 

 total revenue is equal to the ex-vessel price times 

 the catch. In the case of an individual fisherman, it 

 can normally be assumed that the price is constant 

 over all catch ranges. This is because the catch of 



FIGURE 4. — Total catch in the fishing period with respect to the 

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

 that always result in the maximum number of hauls. 



an individual fisherman is relatively small 

 compared with total landings in the fishery and 

 will, therefore, not have a significant influence on 

 the prevailing ex-vessel prices. 



TR = pL 



(14) 



where TR = total revenue 



p = ex-vessel fish price (per pound round 

 weight). 



Total fishing costs are comprised of fixed in- 

 vestment costs, trap hauling costs, and trap costs: 



TC = I K 



H K + ST 



(15) 



where TC = total fishing costs 



fixed costs (e.g., vessel depreciation, 



insurance, routine maintenance) on 



equipment capable of K hauls in D 



days 



costs of K hauls 



costs of traps 



unit cost (depreciated value and 



maintenance cost) of a trap for the 



fishing period {D days). 



l K 



8T 



S 



Trap hauling costs are treated as a constant in 

 the model because the number of hauls is held 

 constant. It is recognized that trap hauling costs 

 are dependent on factors such as fishing depth and 

 the distance traps are set from port as well as the 

 number of trap hauls. This model assumes these 

 factors are relatively constant. In the case of 

 Florida spiny lobster fishing, this may not be too 

 unreasonable an assumption because fishermen 

 customarily fish the same area for considerable 

 periods of time. When the assumption does not 

 hold, neither does the assumption about a con- 

 stant maximum number of hauls. 



Since the model is an analysis of changes in soak 

 time and traps fished, the constant costs in the 

 model (I K andH K ) play minor roles. It is assumed 

 that with the profit-maximizing soak time and 

 number of traps that total revenue will be greater 

 than total costs. If total costs were greater than 

 total revenue for all soak times and number of 

 traps fished, then presumably fishermen would 

 stop fishing to avoid incurring continuous losses. 

 Profit (77) is defined as total revenue (Equation 

 (14)) minus total costs (Equation (15)): 



7T = pL 



I K - H K - 8T. 



(16) 

 215 



