ROTHSCHILD: DEFINITION OF FISHING EFFORT 



other ground such as the tuna grounds off the 

 west coast of Africa. 



The third part of the paper considers, given 

 the possibihty that inputs and outputs can be re- 

 lated and that decision skill can be judged, that 

 different fishermen apply different criteria to the 

 signals that they obtain from their decision en- 

 vironment. This question is discussed in terms 

 of maximizing catch versus minimizing risk in 

 attaining the catch. One of the main conclusions 

 that can be derived from the following discus- 

 sion is that advances toward the management of 

 fisheries as a total system which considers the 

 strategic, tactical, and operational hierarchies 

 and the flow of information and material among 

 these are not limited by analytic techniques. The 

 limitation arises from a lack of explicit formula- 

 tion of the kinds of data needed for the develop- 

 ment of a total management system. 



INPUT-OUTPUT ANALYSIS 



Let us contrive a simple production function 

 problem in a linear-programming context. This 

 approach is treated in some detail by Dorfman, 

 Samuelson, and Solow (1958). We should men- 

 tion that the linear-programming technique is, of 

 course, not without assumptions, and these are 

 discussed in any operations research text (for 

 another application of linear programming in 

 salmon management see Rothschild and Balsiger, 

 1971). Violations of the assumptions required 

 for the linear-programming model are usually 

 handled by other techniques in mathematical 

 programming theory, but these are, in general, 

 computationally more difficult. In order to pro- 

 vide a semblance of realism to the problem, we 

 use some now somewhat outdated data provided 

 in Table 7 of Green and Broadhead (1965). We 

 begin by assuming we have a fleet of 300-, 400-, 

 and 500-ton seiners. The capacity of the fleet 

 is calculated in Table 1. 



The capacity for each size class of boat is an 

 input in the production function. We also need 

 to supply as inputs to the production function 

 some raw material in the form of fish. Let us 

 say that we are limited to 90,000 tons of yellow- 

 fin tuna and 120,000 tons of skipjack tuna. Then 

 the objective of production is to maximize profits 



Table 1. — The capacity in tons of a hypothetical tuna 

 fleet in terms of various size classes of fishing boats. 



by maximizing the objective function: Z = 

 8.65/fn + 7.32/^12 + 10.66/721 + 9.01/^22 

 + l.lbHai + 6.53H32 where the Hi/s correspond 

 to the ith boat size (/ = 1, 2, 3; where the inte- 

 gers refer to 300-, 400-, and 500-ton boats, re- 

 spectively) and the yth species (j = lisyellowfin 

 tuna and / = 2 is skipjack tuna). The coeffi- 

 cients in the objective function correspond to the 

 weighted average profit per ton for the jth spe- 

 cies caught by the ith boat as deduced from 

 Green and Broadhead. Now with respect to the 

 allocation of two scarce inputs — the capacity of 

 various size vessels in the fleet and the catchable 

 stock of the two species — to the production pro- 

 cess, the capacity of the fleet generates the fol- 

 lowing set of constraint equations: 



Hn + Hri ^ 23,460 tons (capacity of small 

 boats) 



H21 + H22 ^ 85,140 tons (capacity of me- 

 dium boats) 



Hii + Hi2 ^ 31,840 tons (capacity of large 

 boats) 



whereas the stock inputs (viz. the catch quotas) 

 generate the following set of constraints: 



Hn + Hn + H,x ^ 90,000 tons ("quota" of 



yellowfin tuna) 

 Hn + H22 + ^32 ^ 120,000 tons ("quota" 



of skipjack tuna). 



Because different size boats catch different pro- 

 portions of yellowfin and skipjack, the ratio of 

 these species in the catch of each size class of 

 boat is essentially a function of the configuration 

 of the boat and its equipment. We can thus con- 

 sider the ratio of skipjack to yellowfin as a tech- 

 nological characteristic of the boat's size class 

 and in order to maintain the character of the 

 technology, we use the percentages of yellowfin 

 in the catch as g-iven by Green and Broadhead 

 (300-ton boats, 577c; 400-ton boats, 48%; and 



673 



