SIEGEL ET AL LINEAR PROGRAMMING APPROACH 



short run corresponding to the level of output that 

 can be produced as determined by market condi- 

 tions, input prices, technology, vessel hold space, 

 and a normal fishing pattern. In effect, economic 

 capacity, other things being equal, moves with 

 price. If prices rise, capacity or output of those 

 vessels already in the fishery will be expected to 

 increase. If prices drop, it will fall.^ 



Conversely, if the catch per unit effort increases, 

 and factor costs and output prices remain un- 

 changed, then capacity rises. The important point 

 to note about the economic concept of capacity is 

 that it is not necessarily the full utilization of the 

 hold space of a fishing vessel. If there are changes 

 in cost conditions, market prices, and stock abun- 

 dance, then capacity output will also change. 

 Thus, the technical notion of capacity described 

 what can be produced based on the physical 

 characteristics of a fishing vessel and the fleet. 

 This concept, however, does not incorporate con- 

 straints on output or the quantity of landings be- 

 cause of economic or environmental factors. In 

 contrast, the economic concept of capacity de- 

 scribes what will be produced given technical rela- 

 tionships, factor prices, and product price informa- 

 tion, and it is essentially what is implied in the 

 FCMA regarding the "extent to which the (physi- 

 cal) capacity will be utilized." 



The definition of fleet capacity used hereafter in 

 this report is as follows: Capacity is the amount of 

 fish that the fleet is expected to harvest during a 

 specified period with the existing stock of capital 

 (vessels and gear) and technology, given catch 

 quotas, processing capabilities, and market condi- 

 tions. Clearly, the expected domestic catch is 

 synonymous with the "extent to which" notion 

 contained in the Act, and both of these are 

 synonymous with the notion of short run economic 

 capacity as defined above. 



SPECIES ALLOCATION OF 



CAPACITY USING A LINEAR 



PROGRAMMING (LP) FRAMEWORK 



This section outlines an approach that can be 

 used to estimate short-run capacity (output) in a 

 multispecies fishery. 



The LP Problem for 

 a Multispecies Fishing Fleet 



A complete generalization of the problem of es- 

 timating the "extent" or the expected catch of the 

 fleet is to determine the allocation of resources 

 (over species, vessel category, fleet capacity, 

 fishing area, and time period) that maximizes a 

 stated objective. The following LP model is based 

 on a model formulated by Mueller.^ 



The statement of the objective function and the 

 associated constraints of the model are presented 

 below; 



Maximize Z = S PjjfL„—ll Cij,Ljj, (1) 



or Z = S L,j, (Pjjt—Ciji) 



i.J.I 



where Z = net revenue received at the harvest- 

 ing level 



L,„ = pounds of species; in area / landed in 

 a directed fishery for that species 

 during period / 



P , = revenue realized per pound of species 

 / landed in a directed fishery for 

 species ; in area j during period t 

 (includes value of bycatch) 



C,,, = cost associated with catching a 

 pound of species ; (and its associated 

 bycatch ) in area j during period t in a 

 directed fishery for species (. 



Equation (1 ) is the objective function to be 

 maximized. It shows the number of pounds of each 

 species that should be caught in a directed U.S. 

 fishery in each area during a particular time 

 period in order to maximize net revenues. These 

 net revenues include the value of the target 

 species and the associated bycatch. In this LP 

 problem formulation, the price per pound landed 

 and cost per pound landed are invariant with the 

 quantity of output.*^ However, these can be al- 

 lowed to vary. 



■•This assumes that there is no entry or exit in a fishery during 

 a given fishing season. If prices rise, vessels may shift from other 

 fishenes; but it is not clear whether the shift will occur in the 

 current or following season. 



■■^Mueller, J. J. 1976. A linear programming discussion 

 model for maximizing the net revenues from a multiple species 

 fishery. Unpubl. manuscr., 13 p. National Marine Fisheries Ser- 

 vice. Federal Building. 14 Elm Street, Gloucester. MA 01930. 



'An alternative formulation of the objective function could 

 involve substitution of a demand function for a given price in 

 each time period. In addition, instead of the assumption of a 

 constant average cost per pound of fish landed, costs could be 

 allowed to vary with the quantity offish landed and with the 



427 



