The parameter ySj is a little more difficult to 

 understand. In the context of the model, fSi is the 

 constant that relates marginal yield correspond- 

 ing to two successive units of effort. By appropriate 

 manipulation of Equation (1) we can derive the 

 following expression: 



i3, = 



ay 

 dE 



ay 



dE 



E+ 1 



(17) 



Rational physical arguments may be used to 

 show that ^1 is bounded by and 1 (0<yQi <1). The 

 law of diminishing returns provides the simplest 

 argument, although there are others. Never- 

 theless, whatever the interpretation of yQi, sen- 

 sitivity of yield to the parameter can be expressed 



as: 



s(y\(3,) = 



-E 



^:'-l 



(18) 



Since we have already established 0</3i<l, 

 Equation (18) can be sketched as shown in Figure 

 2. 



Yield is not very sensitive to ^i for small values 

 of ^i( ~0). The sensitivity increases hyperbolically, 

 however, asymptotically approaching infinity as 

 ^1 approaches the value unity. 



Griffin's estimate of ^Sj is 0.995701. This is about 

 as close as one could get to the most sensitive 

 region in Figure 2. For a value of efforts of 260.8, 

 the sensitivity is -125.63. Thus any small 

 misspecification of /3i would produce very large 

 errors in yield estimates. 



It has already been shown that the parameter /3i 

 is related to marginal product of effort. At this 

 point I question the assumption of fii as being a 

 constant parameter. The marginal product of ef- 

 fort in any fishery is intimately related to stock 

 and fleet characteristics. Realistically, one would 

 expect marginal product and therefore its ratio to 

 vary over time. Even if one could consider f3i to be a 

 constant over 1 yr, it would most certainly change 

 over the course of the 12 yr that were used to 

 estimate the given value (Griffin et al. 1976). Since 

 I have already shown ^i to be the most sensitive 

 parameter of Griffin's equation, any misspecifica- 

 tion or future change of (S^ would have enormous 

 consequences on yield estimates. 



Thus a user of Griffin's equation, who assumes a 

 value of (Si based on previous estimates of stock, 



976 



125.63-- 



FlGURE 2.— Sensitivity (S) of yield to parameter /i,; i.e., the 

 percentage change in yield corresponding to a 1% change in /S,. 



effort, etc., may make incorrect predictions in the 

 face of changing conditions. This observation se- 

 verely limits the applicability of Griffin's equation 

 for management purposes. 



Acknowledgments 



I wish to express my thanks to Lynn M. Pulos 

 who carefully critiqued several drafts of this paper. 

 Her patience is much appreciated. 



Literature Cited 



Christmas, j. y, and d. j. etzold (editors). 



1977. The shrimp fishery of the Gulf of Mexico United 

 States: A regional management plan. Gulf Coast Res. 

 Lab., Tech. Rep. Ser. 2, 128 p. 



Griffin, w. l., and b. r. Beattie. 



1978. Economic impact of Mexico's 200-mile offshore fish- 

 ing zone on the United States Gulf of Mexico shrimp 

 fishery. Land Econ. 54:27-38. 



Griffin, w. l., r. d. lacewell, and J. R Nichols. 



1976. Optimum effort and rent distribution in the Gulf of 

 Mexico shrimp fishery. Am. J. Agric. Econ. 58:644-652. 



