A Stochastic Investment Model 

 for a Survival Conscious Fishing Firm 



Russell G. Thompson, Richard W. Callen, 

 and Lawrence C. Wolken' 



ABSTRACT 



In this study, the stochastic investment model for a survival conscious firm developed 

 by Thompson and George (1970) is extended to talte into account income taxes and 

 depreciation of the capacity. This model is applied to shrimp fishing on the Texas Gulf 

 coast. Values of the parameters, as in the deterministic application by Thompson et al. 

 (1970), were based on proprietory information, current market conditions, and present 

 institutional restrictions. The effect of growth in real per capita income on shrimp 

 prices is estimated, and two different rates of income growth are analyzed. Solutions 

 to six problems based on two different sets of random sequences are computed and 

 discussed. The results indicate the effect of the survival constraint on investment 

 decisions, and the importance of revealed information in decisionmaking. 



INTRODUCTION 



In 1970, Thompson and George formulated a 

 stochastic dynamic investment model for the 

 survival conscious firm, derived the optimal 

 decision rules for investment, and computed 

 solutions to several problems. This model takes 

 into account the probability distribution of the 

 yield (output per unit of capacity) and output 

 price, as well as all of the information known to 

 the decisionmaker at the time of each investment 

 decision. The entrepreneur is initially assumed 

 to be in a financial position where a feasible 

 investment solution always exists if the lowest 

 output price and yield occur in every period of 

 the planning horizon. In the model, the objective 

 of the firm is to maximize expected net worth at 

 the end of the planning horizon. All production 

 expenses, investment outlays, interest costs. 



' Russell G. Thompson is Professor of Quantitative 

 Management Science, University of Houston; Richard 

 W. Callen and Lawrence C. Wolken are Lecturers in 

 Quantitative Management Science. University of Hous- 

 ton. This work was partially supported by the National 

 Science P'oundation GH 59 as a part of the Sea Grant 

 Program for 1970. 



and planned cash withdrawals must be paid 

 for as incurred (or scheduled). 



In this study, the Thompson-George model is 

 extended to take into account income taxes and 

 depreciation. This requires the introduction of 

 another state variable to account for the value 

 of the firm's capital — the investment in 

 capacity. Straightforward extensions of the 

 fundamental constructs (developed by Thompson 

 and George) were required, and are available 

 from the authors upon request. 



Because of the vagaries in fish prices and 

 catches, this model would be expected to be a 

 particularly appropriate decision aid for invest- 

 ments in fishing capacity. There are generally 

 few, if any, alternative uses for specialized 

 fishing equipment. Also, fishermen typically 

 have poor alternative opportunities by which to 

 earn a living. Low prices and small catches 

 would be expected, as a result, to be dreaded 

 much more than high prices and large catches 

 are desired. A sequence of worse than expected 

 net revenues (even in the case of a very favorable 

 expectation) could terminate the existence of 

 the fishing firm. This could well be an unaccept- 

 able risk of failure. Hence, survival of the 

 fishing firm would be expected to be a funda- 

 mental factor influencing the firm's investment 

 decisions. 



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