Random Sequences of Revenues per Vessel 



Sequence No. 2 

 Problem 1 Problem , 



$25,450 

 47,261 

 38,810 

 36,077 



44,747 



$29,920 

 53,546 

 44,589 

 41,719 

 50,495 



It may be helpful to recall that the decision- 

 maker is regarded as being a better than average 

 manager in Problem 3. The 1.5% rate of real 

 economic growth per capita is used in Problems 

 1, 2, and 3; and the 3.3% rate of economic 

 grovrth is used in Problem 4. 



In evaluating the solutions to the first set of 

 four problems in Table 2, the results indicate 

 the profitability of investing in shrimp fishing 

 capacity during the 5-year planning period. 

 The model fisherman opted for investing in 

 fishing capacity in Problem 2, even though he 

 could have left his money in savings at 8.5% 

 interest. Thus, the rate of return over cost from 

 shrimp fishing was greater than 8.5% . In further 

 analysis, it was found to continue to be so until 

 the rate of interest reached 9.5% ; then the rate 

 of return over cost switched in favor of savings. 



The value of better than average management 

 is indicated by the results in Problem 3. There, 

 the average landing per vessel was taken to be 

 one standard deviation (5,731 pounds) greater 

 than in Problem 1. The same amount was 

 invested in the first year; but in the second and 

 third years there were striking differences. The 

 model fisherman bought 5.2 vessels in Problem 

 3, while he did not buy any in Problem 1. He 

 chose to pay off debt in the first problem after 

 the initial investment, since that represented 

 a more profitable use of the money. It may be 

 noticed that the investment upper bound limited 

 the size of the purchases in the first 3 years of 



Problem 3 (and the first year of Problem 1). 

 The marginal value of another vessel was 

 positive; however, the money was not available 

 for investment given the desire to sui-vive. 



Success in shrimp fishing is clearly influenced 

 by the rate of income gi'owth in the economy — 

 compare Problems 1 and 4. In Problem 4, the 

 marginal value of another vessel is almost 

 twice as large in the first year as in Problem 1, 

 and remains large in the second year when the 

 value in the first problem goes negative. This 

 increased growth in per capita income results 

 in an increased ability to invest in the second 

 year in Problem 4 and still further increased 

 ability, at a lower marginal incentive, in the 

 third year. The model fisherman carries a con- 

 siderably larger debt load, as a result of the 

 increased profitability, in Problem 4 than in 

 Problem 1. 



In evaluating the second set of results given 

 in Table 3 and comparing these solutions to 

 the ones in Table 2, only slight differences 

 between the results may be noticed. Somewhat 

 less is invested over the planning period in 

 Problem 3 in the second case than in the first. 

 Also, a slightly larger debt load was generally 

 carried in most of the planning period. Of 

 course, the marginal investment incentives 

 were the same in both sets of problems; they 

 are based on expected values. Vagaries in land- 

 ings seem to be much more important than 

 unexpected variations in price. 



LITERATURE CITED 



THOMPSON, RUSSELL G., and MELVIN D. GEORGE. 

 1970. A Stochastic Investment Model for Survival 

 Conscious Firm. Presented at Winter Meetings of the 

 Econometric Society, Detroit, December, 1970. 



THOMPSON. RUSSELL G., RICHARD W. CALLEN, 

 and LAWRENCE C. WOLKEN. 1970. Optimal Invest- 

 ment and Borrowing Decisions for a Model Shrimp 

 Fishing Firm, Texas A&M University, Sea Grant 

 Bulletin No. 205, .A.pril. 



BOX, G. E. P.. and MERVIN E. MULLER. 1958. A 

 Note on the Generation of Random Normal Deviates, 

 The Annals of Mathematical -Statistics, Vol. 29, June, 

 pp. 610-611. 



119 



