Cross Section Production Functions for North 



Atlantic Groundfish and Tropical 



Tuna Seine Fisheries 



Ernest W. Carlson' 

 ABSTRACT 



This paper explores the use of cross section production functions to estimate the 

 fishing power of individual vessels. The problems addressed are: The proper measurement 

 of output; the measurement of technological change, and the effect of location, crew- 

 size and important vessel characteristics. 



Regression analysis upon data from the North Atlantic groundfish fishery and the 

 tropical tuna seine fishery yielded highly significant results. Many of the hypothesized 

 relationships are measurable and stable with relatively small errors. The tests indicate 

 that: there are better measures of output then total pounds; fishing time is measured 

 better using days absent rather than days fishing; the use of more vessel characteristics 

 improves explanatory power; crew size can be an important variable; the effects of 

 location can be measured; and technological change can be measured. 



The production functions measured can then be used as inputs in devising 

 management schemes. 



INTRODUCTION 



One of the more difficult problems in the 

 management of fisheries has been the measure- 

 ment of vessel productivity. If the vessels in a 

 fleet were physically homogeneous and utilized 

 for the same amount of time and if no learning 

 took place, the problem of measuring productivi- 

 ty indices would be less difficult. The problem 

 does exist, though, because vessels are far from 

 homogeneous. For example, a typical fleet may 

 have vessels that are 10 or more times larger 

 than the smallest vessels in a fleet. Obviously, 

 under such conditions there will be serious 

 errors introduced if attempts are not made to 

 measure the productivity of different vessels. 



To handle this and related problems, econo- 

 mists have developed techniques of measurement 

 that fall into a general category called production 

 functions. One of the important attributes of 

 using a production function is that it allows 

 the simultaneous measurement of as many 



' Economist, Economic Research Laboratory. National 

 Marine Fisheries Service. 



parameters of fishing power as may be thought 

 to be important in its determination. According- 

 ly, production functions were estimated using 

 data from the New England trawl fleet and the 

 tropical tuna seine fleet. Many problems were 

 considered in arriving at a "best" production 

 function for these fisheries. 



THE PRODUCTION FUNCTION FOR 

 A FISHERY 



The basic assumption of this paper is that a 

 production function can adequately describe 

 the relationship between inputs and outputs in 

 a fishery. The production function is a technical 

 or engineering relation between inputs and 

 outputs and is the base upon which the economic 

 theory of supply is built. Since it is an engineer- 

 ing relationship, considerations such as prices 

 and costs are not relevant to the production 

 function itself. The schedule of maximum output 

 for given inputs is the production function we 

 are trying to measure. 



The cla-ssical production function for the 

 individual firm is usually presented as follows: 



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