Variations in landings per unit effort, which 

 were found to be highly correlated for the Texas 

 and Gulf-South Atlantic fisheries, are still 

 regarded by biologists as being largely random. 

 Thus, to remove the effect of landings on price, 

 landings were specified to be equal to the mean 

 value observed for the Texas fishery in the 

 period 1958 through 1967. Hence, the price 

 estimating equation with an adjustment to a 



1969 base year was as shown below. 



(5) Inp, =-1.332 + 1.175 In y, 



To use this equation, the index of real per 

 capita income had to be projected for the years 



1970 through 1974. This was done by regressing 

 In yt on time, t. for the years 1953 through 

 1960, and also for the years 1961 through 1968. 

 The following two income projection equations 

 were developed for the period t = 1970, 1971, 

 . . ., 1974. 



Specification I: 1.5% rate of income growth 



(6) Iny, = 4.94 + .015t 



Specification II: 3.3% rate of income growth 



(7) Iny, = 4.94 + .033f 



By substituting the desired specification 

 from (6) into (5), the price projection equation 

 was obtained. The effective expected real shrimp 

 price, a,, was 0.65 of the antilog of/),. To convert 

 to money terms, the projected prices were 

 multiplied by the consumer price index value 

 for 1969, 1.277, and by a price inflating factor 

 of 3% per year thereafter. In Table 1, Pi denotes 

 the price reflecting the high rate of income 

 growth and p, the low rate. 



For the first set of four problems, the estimate 

 of the owner's lowest annual revenue per 

 vessel, Li, was found by taking the lay residual 

 of the product of the 1969 shrimp price, aeg, 

 and the projected lower bound for landings per 

 vessel. This lower bound was taken to be 3.4 

 standard deviations (in t units for 11 degrees 

 of freedom) below the mean landing per vessel 

 of 57,560 pounds with the sample standard 

 deviation being 5,731 pounds. Thus, the prob- 

 ability of the landings per vessel being greater 

 than this lower bound (assuming this to be a 

 valid probability basis) is greater than 0.99. 

 Moreover, since the growth rate in real per 

 capita income is not taken into account in L,, 



the probability of revenue per vessel falling 

 below the implied estimate of the owner's lowest 

 annual revenue per vessel (where the price is 

 projected under either specification) decreases 

 steadily as the planning period unfolds. In 

 other words, the estimate of Lf is very conserva- 

 tive for the year 1970 and becomes increasingly 

 conservative thereafter in the planning period.-' 



For the second set of two problems in which 

 the shrimp price is random as well as the 

 landing per vessel, the same value was used for 

 the owner's lowest annual revenue per vessel. 

 This resulted in a slightly smaller probability 

 of survival than in the first four problems 

 (because of the additional randomness in the 

 price), but one still greater than 0.99. Thus, in 

 the interest of simplicity, the same value of 

 Lr was used in both sets of problems. 



Knowledgeable industry representatives (who 

 were consulted with regard to the above specifi- 

 cations) indicated a 5-year survival period 

 would be especially meaningful for firms operat- 

 ing the 73-foot trawlers. Accordingly, two 5- 

 year sequences of random revenues per vessel 

 were developed with only the landing per vessel 

 being I'andom in the first sequence. Landings 

 per vessel were regarded as independent of 

 price, since the fishery is relatively competitive; 

 moreover, for the period studied, per vessel 

 landings for the cooperating firms were not 

 highly correlated with landings per unit of 

 effort in the Texas fishery^ (r^ = 0.16). Using 

 the regression estimate for price in each year 

 1970 through 1974 and the estimated standard 

 error of the regression, and also using the sample 

 mean and standard deviation for landings per 

 vessel of the cooperating firms, the random 

 prices and landings per vessels were calculated 

 as follows: (1) By use of the Box-Muller (1958) 

 method, normal random deviates for prices and 

 landings per vessel were independently gener- 

 ated; and (2) the products of these two random 

 variables were adjusted for the lay and expected 

 changes in the purchasing power of money. The 

 following random sequences were accordingly 

 obtained and used in the analysis. 



^ To have a probability support at L,, this small 

 probability of non-survival is implicitly assumed to be 

 insurable. 



^ Landings per unit effort in the Texas Fishery are 

 highly correlated with those for the Gulf and South 

 Atlantic. 



118 



