SIEGEL ET AL LINEAR PROGRAMMING APPROACH 



'Based on 1970-74 average 



species in the otter trawl fishery resulting from 

 the entry of foreign effort in these fisheries in the 

 late 1950's and early 1960's. 



The LP model formulated in the previous sec- 

 tion required data on species, prices, harvesting 

 costs, bycatch ratios, and physical capacity esti- 

 mates for both the harvesting and processing sec- 

 tors. Data are generally available for these items 

 except for harvesting costs. In the absence of har- 

 vesting cost data, the objective function in the 

 model was specified to only maximize gross rev- 

 enues. Because of this, the solution variables 

 would probably be overestimates of actual ex- 

 pected catches. 



In this report the method of incorporating cost 

 factors is to deflate the peak CGRT by an index of 

 relative species abundance (Clark and Brown 

 1977). The index of stock abundance is being used 

 to adjust the expected level of catch for changes in 

 cost conditions for the 1955-77 period. Since the 

 level of catch is, among other factors, a function of 

 abundance, any declines m abundancfe would 

 be expected to result in a lower level of catch (other 

 things being equal). Reductions in abundance, 

 therefore, would be expected to result in declining 

 CGRT and increased costs per unit of output. A 

 more realistic measure of factor productivity 

 would be catch per unit of effort; this information 

 is not available. 



Data in Table 2 indicate that GRT has not 

 changed significantly since 1955 for this otter 

 trawl fishery. The assumption was made that the 

 number of days fished per GRT has not changed.' 

 The year 1957 was chosen as the base year because 



CGRT reached a maximum value and stock abun- 

 dance was probably relatively high. Table 2 also 

 shows an index of stock abundance for the Interna- 

 tional Commission for the Northwest Atlantic 

 Fisheries (ICNAF) designated subarea 5 and 

 statistical area 6 for finfishes and squids. 



In order to devel op a measure of expected output 

 relative to 1957, it is noted that catch in sub- 

 sequent years will vary as a function of fishing 

 effort and stock abundance. If the catchability 

 coefficient relative to GRT can be assumed to be 

 the same, at least as a first approximation for each 

 year, then the catch in any year is: 



II 



^0 



where T, is the GRT in the iih year, and T„ and €„ 

 are, respectively, the GRT and catch for the year 

 1957." Furthermore, it is assumed that catch 

 would depend on the abundance of the stock and, 

 therefore, the catch in any vear should be modified 

 by: 



where A, denotes the abundance in the ;th year 

 and A„ the abundance in the base year (1957). 



Thus, an estimate of expected output relative to 

 the base year is: 



^Data are not available to verify this assumption. 



^Using this approach, it is necessary to choose a base year. Asa 

 result, physical capacity and economic capacitv were identical 

 for 1957. 



429 



