Table 3. — Solutions to two survival problems in table 1; shrimp prices and landings per vessel are random. 



To reflect inflation, the purchase price of new 

 vessels was specified to increase at 3% per year. 

 This rate is 2% below reported price trends, 

 which include costs of technological improve- 

 ments. Newer vessels have been powered by 

 larger engines. This has allowed for larger 

 trawls to be towed at faster rates. This rate of 

 improvement in technology is believed to have 

 increased investment costs by 2% per year. 



From the cost records of the cooperating 

 firms, the annual cost of operating a 73-foot 

 trawler was found to be $30,000 in 1969. This 

 cost figure includes an allowance for overhead 

 and insurance. Representatives of the firms 

 interviewed indicated these costs have increased 

 3% per year in recent years. Thus, the annual 

 production cost per vessel, t,, was specified to 

 be 30,000 (1.03)', 



Straight line depreciation methods were used 

 for tax purposes with an 11-year depreciation 

 period being used for a fully outfitted vessel. 

 This average was estimated on a value weighted 

 basis from the records of a number of firms. 

 The reciprocal of this figure, 0.091, was the 

 value used in the depreciation function. 



Income is the sum of the revenues received 

 (by the owner after the "lay") less operating 

 costs, interest costs (or plus interest earnings), 

 and taxes. The income tax rate, which is denoted 

 by f, was taken to be 25% of the taxable income. 

 This rate was paid in the late 60's by a number 

 of the firms studied. 



In shrimp fishing, the captain and first mate 

 on a vessel are commonly paid on a "lay" basis 

 wherein they receive for services rendered a 



percentage of the revenue earned by the vessel. 

 The header, who is the third crew member, is 

 typically paid on a per box basis; his wages are 

 included in the production cost per vessel. For 

 73-foot vessels, the "lay" for the captain and 

 first mate is commonly 35% (with the owner 

 getting in effect 65% of the ex-vessel price); they 

 typically pay for all of the groceries. 



In interviewing the cooperating firms, the 

 relative resale value of the vessels sold was 

 found to be fairly well approximated (for vessels 

 5 to 6 years old) by summing the accumulated 

 depreciation fractions with an appropriate ad- 

 justment for technological improvement. This 

 procedure, which implies that the resale value 

 of a vessel 5 years old would be 65% of the 

 purchase price, was used as the basis for specify- 

 ing (3 to be equal to 0.65-. 



To project per vessel expected revenue re- 

 ceived by the owner, the log of the real shrimp 

 price received by the cooperating firms, P,, was 

 regressed on the log of the index of real per 

 capita income (in the United States after taxes), 

 yt, and the log of per unit effort landings, h, 

 caught in depths beyond 10 fathoms off the 

 Texas coast. (See the earlier study by Thompson 

 et al. (1970, p. 12) for data.) The estimated 

 regression equation was as follows: 



(4) In p, = -4.571 + 1.175 In y, 



(f = 3.6) 



R' = .148, Oe = .0888. 



.379 In/r, 

 (f = 3.5) 



- This approximating procedure was necessary, since 

 the vintage was not accounted for in the model. 



117 



