FISHERY BULLETIN VOL. 72, NO. 1 



TT = pKx -C = pKgiX,K) -Kn (4) 



5 277', 7r<0 



(5) 



In the above system, X is the biomass; K 

 equals the number of homogeneous operating 

 units or vessels; x is the catch rate per vessel; 

 C is total industry cost (in constant dollars) or 

 total annual cost per vessel multiplied by the 

 number of vessels; ^ is equal to total annual cost 

 per vessel (in constant dollars) or opportunity 

 cost;' 77 is industry profit in excess of oppor- 

 tunity cost; p is the real ex-vessel price; and 

 5 J , 5 2 represent the rates of entry and exit of 

 vessels, respectively. Equation (1) represents 

 the biological growth function in which the 

 natural yield or net change in the biomass {X) 

 is dependent upon the size of the biomass, X, 

 and the harvest rate, Kx. X reflects the influence 

 of environmental factors such as available 

 space or food, which constrain the growth in 

 the biomass as the latter increases. The harvest 

 rate or annual catch, Kx, summarizes all growth 

 factors induced by fishing activity. Equations 

 (2) present the industry and firm production 

 function for which it is normally assumed that 



dg 

 dX 



= g,>0 and f^=g^<0:^ 



dg 

 bK 



In other words, 



catch per vessel increases when the biomass 

 increases and declines when the number of 

 vessels increases. Equations (3) and (4) are the 

 industry total cost and total profit function, 

 respectively. Equation (5) is a very important 

 equation since it indicates that vessels will 

 enter the industry when excess industrial 

 profits are greater than zero (i.e., greater than 

 that rate of return necessary to hold vessels 

 in the fishery, or the opportunity cost) and 

 will leave the fishery when excess industrial 

 profits are less than zero (i.e., below opportunity 

 cost). 



■* Opportunity cost is defined as the necessary payment 

 to fishermen and owners of capital to keep them employed 

 in the industry or fishery compared to alternative employ- 

 ment or uses of capital. 



■'•In some developing fisheries, it is possible that .i;2>0. 

 For example, in the Japanese Pacific tuna fishery, inter- 

 communication between vessels may increase the catch 

 rate as more vessels enter the fishing grounds. 



The equilibrium condition for the industry 

 (n = 0) may be formulated as shown below: 



P = 



77 



g{X,K) 



(6) 



Equation (6) merely stipulates that ex-vessel 

 price is equal to average cost per pound of fish 

 landed (i.e., no excess profits). 



There are two important properties of the 

 system outlined in (1) - (5). First, the optimum 

 size of the firm is given and may be indexed by 

 77. Thus, the firm is predefined as a bundle of 

 inputs." Second, the long-run catch rate per ves- 

 sel per unit of time is beyond the individual 

 firm's control." It is, in effect, determined by 

 stock or technological externalities.** Finally, 

 we are assuming that the number of homo- 

 geneous vessels is a good proxy for fishing 

 effort. Alternatively, we may employ fishing 

 effort directly in our system by determining 

 the number of units of fishing effort applied to 

 the resource per vessel. This will be discussed 

 below. 



A QUADRATIC EXAMPLE OF 

 THE RESOURCE USE MODEL 



By combining the more traditional theories 

 depicting the dynamics of a living marine re- 

 source with some commonly used economic 

 relations, we may derive a quadratic example 

 of the general model specified above. This 

 example effectively abstracts from complications 

 such as ecological interdependence and age- 

 distribution-dependent growth of the biomass 

 on the biological side and, furthermore, assumes 

 the absence of crowding externalities (i.e., ^2 ~ 

 0) in the production function on the economic 

 side. 



'' In other words, because we are dealing with a long-run 

 theory of the industry, we are assuming that variations 

 in output result from the entry or exit of optimum-sized 

 homogeneous vessels. 



^ We have implicitly assumed that such short-run 

 changes as longer fishing seasons, etc., are all subsumed in 

 a long-run context. Normally longer fishing seasons, for 

 example, do not change catch rates per unit of time fished; 

 nor do they change costs per unit of time fished. They 

 do, however, change the effective level of K. 



* A technological externality exists when the input into 

 the productive process of one firm affects the output of 

 another firm. In the context of fishing, an additional firm 

 or vessel entering the fishery will utilize the biomass 

 (as an input) and, as a result, in the long run will reduce 

 the level of output for other vessels in the fleet. (See 

 Worcester (1969)). 



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