FISHERY BULLETIN: VOL. 70, NO. 3 



the costs of their operations — must differ con- 

 siderably. This, of course, in no way invalidates 

 the population dynamics theory and there are, 

 in fact, methods for converting fishing effort, de- 

 fined in terms of the magnitude of the catch, into 

 numbers of fishing boats, etc. There is an exten- 

 sive literature on this subject and, because of 

 this, there is no need to prolong the discussion of 

 this particular aspect of the fishing-effort prob- 

 lem. Rather, we shall concentrate on aspects of 

 the problem of identifying and measuring inputs 

 to the fishing process as well as discussing the 

 methodology of relating the set of inputs to the 

 outputs (the catch), which can, as we will see 

 by the ensuing discussion, be treated in terms of 

 several species and even, if necessary, in terms of 

 strata (such as, for example, size classes) within 

 several species. These aspects of the problem 

 simply relate to the theory of production func- 

 tions. Production functions have seldom been 

 treated in fisheries, but when they have, they 

 have been approached primarily from a regres- 

 sion analysis point of view. It is not clear, even 

 given that we meet the assumptions of the 

 estimation procedures and thus obtain cred- 

 ible statements on the "good properties" of 

 the estimation procedure, that the curve fitting 

 technique can do much more than describe, in 

 an artificial way, the status quo; there is no in- 

 herently good advice in the curve fitting pro- 

 cedure on optimality; optimality must be im- 

 plicitly assumed. What is needed are techniques 

 of finding those combinations of inputs that pro- 

 duce extrema in the outputs, as well as to de- 

 termine the sensitivity of this input-output sys- 

 tem to changes in the magnitude of the inputs, 

 and a reevaluation of the input-output system 

 which will acknowledge the stochastic aspects 

 of the decision process. 



Our analysis of the fishing eflfort problem is 

 divided into several parts. First, the fishing- 

 eflfort problem is recast as a production function 

 problem whereby valuable inputs to the fishing 

 process are allocated among the outputs of the 

 process in a manner which maximizes profit. In 

 the particular example chosen the inputs are the 

 capacities of three sizes of fishing boats in a fleet 

 and the "catchable stocks" of two species of fish, 

 yellowfin and skipjack tuna, whereas the outputs 



are the catches of the various species in the dif- 

 ferent boats. The components of the yellowfin 

 and skipjack tuna catchable stocks are allocated 

 among the various size vessels in the fleet to max- 

 imize profits. The technique used to explore the 

 maximization of profits is linear programming. 

 The technique enables the simultaneous explora- 

 tion of fleet technological constraints, the inter- 

 action of multiple species as inputs to the de- 

 cision process, and the range within which catch- 

 es can be set without changing the nature of the 

 profit maximization equation. Easy algebraic 

 extensions of the model can be seen to have rather 

 important implications. For example, instead 

 of allocating two species of fish among three boat 

 classes, the stocks of i species can be allocated 

 among ./ classes of boats and k fishing nations. 

 The ease of such an extension may, however, be 

 somewhat deluding, particularly because of the 

 difl^iculty in defining appropriate coeflRcients and 

 constraints respecting the allocation among the 

 k nations. Nevertheless the difliculty does not 

 preclude solution and furthermore placing the 

 problem in this context enables a much needed 

 formulation of the problem of allocation of fish 

 stocks among countries. 



Most input-output analyses involve physical 

 inputs and outputs. This was true in the ex- 

 ample cited above. A classic example in fish- 

 eries is that of fishing power which is frequently 

 related to fishing vessel horsepower. There are 

 many instances, however, where the physical in- 

 puts (horsepower, fleet capacity, etc.) are less 

 important than those related to the skill utilized 

 by the fisherman in making managerial decisions 

 such as where to fish, when to fish, when to stop 

 fishing, etc. So, in the second part of this paper 

 we consider the development of a decision theory 

 model for adjudging fisherman skill in a "real 

 world" probabilistic environment and show how 

 the quality of the fisherman's skill in decision 

 making relates to the entropy of his decision en- 

 vironment. Many important applications of this 

 theory beyond the examples utilized in the text, 

 such as the decision of whether to fish species a 

 or species b when both species are available or 

 whether to fish on one ground such as the eastern 

 tropical Pacific tuna grounds or to move to an- 



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