FISHERY BULLETIN: VOL 77. NO 



Table 7. — Results of the base mode! showing estimated U.S. catches and surpluses in the 

 otter trawl fisheries in ICNAF Areas 5 and 6. Harvesting capacity - 325 million pounds 

 (147.565 tl; gross revenues = $68,605,600. 



Species 



Directed 

 catch 



Bycatch 



Quota 



Estimated 

 surplus 



Actual 

 surplus 



The results of the model (Table 7) indicate that all 

 of the cod, haddock, redfish, pollock, yellowtail 

 flounder, and other flounders be allocated for ex- 

 clusive U.S. exploitation since the sum of the di- 

 rected catches and the bycatches for these species 

 are equal to the quotas. 



The results from the model did identify the exis- 

 tence of surpluses for silver and red hake, Atlantic 

 mackerel, squid, and other finfish. Coincidentally, 

 the species or species groupings for which 

 surpluses were identified in the Preliminary 

 Management Plans (PMP'sl for the Fishery Con- 

 servation Zone in the northwest Atlantic were for 

 these same species identified by the model. All of 

 the surpluses, except for Atlantic mackerel, are 

 larger than the actual surpluses specified in the 

 PMP's. (These surpluses appear in column 7 of 

 Table 7.) This would be expected since the model 

 only considered the otter trawl fleet capacity in 

 New England and did not include harvesting 

 capacity by other gear types in New England and 

 in the Mid-Atlantic area. 



An important implication of the optimal solu- 

 tion for the LP model was the calculation of 

 shadow prices for certain species for which the 

 constraints were binding (i.e., there were zero 

 surpluses).'^ The optimal solution indicates that 

 the quotas for Atlantic cod, haddock, redfish, pol- 

 lock, yellowtail flounder, and other flounders were 

 harvested. In addition, the entire harvesting 

 capacity was utilized. Therefore, all of these 

 species quotas were binding constraints and the 

 resources had positive shadow prices in the opti- 

 mal solution. Furthermore, harvesting capacity 

 was also a binding constraint. Shadow prices are 

 shown in Table 8. For the species in excess supply 



Table 8. — Shadow prices for binding constraints. 



Resource 



Stiadow pnce (S/lb) 



i^Shadow prices show the changes in the objective function for 

 a unit change in the constraint (see column RHS in Table 6). 



432 



Atlantic cod 



Haddock 



Redfisti 



Pollock 



Yellowfail flounder 



Othier flounders 



Harvesting capacity 



0-14 

 0,32 

 0.02 

 0,01 

 0,30 

 19 

 12 



(as evidenced by surpluses) there are no shadow 

 prices. This is to be expected since the correspond- 

 ing shadow price is zero because the excess supply 

 is of no value to the U.S. fleet if it cannot be har- 

 vested and sold. 



In this particular problem, the shadow price for 

 cod can be interpreted as follows: if the Atlantic 

 cod quota was increased by 1 lb, the objective func- 

 tion would increase by 14 cents. This 14 cent,>^ 

 includes the imputed value of Atlantic cod 

 (shadow price) and the other species caught as 

 bycatches with cod less the value of a pound of 

 lower valued species that the new mix replaces. As 

 can be seen from Table 8, the shadow prices vary 

 since the exvessel prices shown in the simplex 

 tableau (Table 6) are different. In the optimal so- 

 lution, the shadow price for harvesting capacity is 

 lower than most of the other species in Table 8. 

 This is because if the harvesting capacity was in- 

 creased by 1 lb, the only species available to har- 

 vest are the lower valued species. 



Shadow prices play an important role in the 

 development of resource management strategies. 

 For example, a decision to rebuild the stock for a 

 particular species could be based on the shadow- 

 price that indicates the greatest return when a 

 constraint is increased by one unit. The LP model 

 in this paper, given the shadow prices from the 

 optimal solution, shows that in the multispecies 

 otter trawl fishery, cod, haddock, and yellowtail 



