X =f(l,k\t), 



where x = output, 



I = labor, 



k = capital, 



t = natural resources. 



Output (x) is measured as the flow of goods and 

 services during an accounting period. The input 

 variables (/, k, t) are the various kinds and 

 qualities of labor, capital, and natural resources 

 that go into producing the output. It is assumed 

 that a given set of inputs produces as much 

 as possible. 



The estimation of the parameters of the 

 production function is accomplished by running 

 a regression upon a cross section of fishing 

 vessels. A cross section is a sample of the vessels 

 in a fishery for a fixed time period. The para- 

 meters estimated from the cross section will give 

 the marginal contribution to output of each 

 variable being used to explain output. 



We will discuss the variables that will be 

 used in the production function in the following 

 section. 



Output in a Fishery 



Most systems for measuring relative vessel 

 productivity have, ultimately, related output to 

 some fishing vessel characteristic. The basic 

 problem with this is that output, when using 

 commercial landings statistics, is a very complex 

 concept. Except in extremely simple fisheries, 

 fishermen do not ordinarily attempt to maxi- 

 mize pounds of fish landed. One working 

 hypothesis is that in all fisheries, the fishermen 

 attempt to maximize their profits. This is not 

 necessarily the same as maximizing total pounds 

 of fish landed. Using total pounds as a measure 

 of output would be an acceptable measure of 

 output (1) where there is a single species 

 fishery or (2) if, in a multispecies fishery, the 

 prices of the target species are approximately 

 the same and the species are equally catchable. 

 In the general case, these conditions are not met. 



How do the fishermen decide where to go and 

 what to catch when there are multiple species 

 in a fishery? Again, the answer to this question 

 is difficult. Let us consider two models of 

 behavior that might help answer this question. 

 In the first type of fishery, the vessel captains 



take into account the species that are available, 

 the grounds where they are available, the prices 

 for which they can be sold, and the expected 

 catch rates for their vessels on the grounds. 

 Integrating all this information, the captain, if 

 he is a profit maximizer, will decide to go to 

 the grounds and fish for the species which pro- 

 vide the highest net profit. His decision may or 

 may not be to fish where the catch rates are 

 highest or for those species that bring the 

 highest prices. 



We have been discussing this as if the choice 

 were always between species. The choice can 

 also be made within a species, such as a decision 

 to fish on local grounds rather than on distant 

 grounds where the catch rates are higher. In 

 this case, the higher catch rates may not offset 

 the extra running time necessary. 



If this abbreviated discussion is an adequate 

 description of how fishermen behave in one 

 type of fishery, then it follows that we may not 

 be able to estimate relative vessel productivity 

 with total pounds, but must rely on some higher 

 order measure such as the value of catch. 



Value was considered by Gulland (1956) as 

 a measure of output and rejected because of the 

 variability of prices. A large part of the vari- 

 ability of fish prices is due to the seasonal 

 availability of the fish themselves with prices 

 moving inversely to availability. We can lessen 

 the objections to value at least partially by 

 using annual data so that the interseasonal 

 effects of availability average out. Another 

 alternative would be the estimation of relative 

 efficiency on a quarterly basis. 



The second type of fishery is one where the 

 location of the fish by species is generally 

 known, but where there is considerable mixing 

 of single species schools in the same area. If 

 locating any school has a low probability per 

 unit time, the fishermen will attempt to catch 

 all that they can of those they do locate. In this 

 case, the fish will be joint products of the fishery. 

 If the fish are equally catchable and their prices 

 are not too different, then total pounds could 

 be the measure of output. If they are not equally 

 catchable, it would take more fishing power to 

 catch one than the other. In such a case, we 

 might have to utilize a modified estimation 

 scheme to arrive at a proper weighting for 

 output. One such scheme will be discussed under 

 the statistical section on tuna. 



43 



