DEVELOPMENT OF THE 

 SURVIVAL MODEL 



In the survival model, the decisionmaker 

 evaluates the worst sequence of net revenues 

 that could occur in every year of the decision- 

 making period. This sequence, in conjunction 

 with the value of the initial investment in 

 capacity and the value of the money account, 

 determine the survivable set of fishing capacity 

 purchases at the beginning of the first year. 

 The decisionmaker selects from this set the 

 investment that contributes the most to his 

 terminal net worth. After the first year and 

 before the second operating year begins, the 

 output price received and the yield obtained in 

 the first year have been observed. This is now 

 a part of the information known to the decision- 

 maker for planning in the second year. The 

 decisionmaker again evaluates the worst se- 

 quence of yields and prices that could occur in 

 every remaining year of the decisionmaking 

 period. This abbreviated sequence is now 

 evaluated in conjunction with the capacity and 

 money position at the end of the first year. It 

 determines the survivable set of capacity pur- 

 chases for the second year. Again, as in the 

 first year, the decisionmaker selects from this 

 second set the investment that contributes the 

 most to his terminal net worth. This procedure 

 is repeated in every year throughout the 

 decisionmaking period. Investment decisions 

 are conditioned by experience, and are not based 

 solely on expected values. 



By definition, the firm survives in a given year 

 if the value of the capacity exceeds the value of 

 the indebtedness. A survivable investment is 

 defined in the following way: the decisionmaker 

 has completed operations in year A--1 and is now 

 planning for year k. He wants to survive above 

 all else during the remaining iV — (k-1) years 

 of the decision period, even if all future yields 

 and prices are the lowest possible. An invest- 

 ment decision in the /fth year, sj^., is said to be 

 survivable if the value of the capacity in every 

 remaining year is never less than the indebted- 

 ness owed (with capacity not being purchased 

 in any of the years after the A-th one and the 

 lowest net revenues being visualized in every 

 year of the yet undisclosed future). 



Under these conditions, a survivable ca- 

 pacity purchase in year A; is found to be 



equivalent to the following one: the product of 

 the capacity units purchased in year A- and the 

 marginal value of capacity calculated under the 

 assumption of the lowest net revenue occurring 

 in every forthcoming year — the marginal cost 

 of capacity visualizing the worst — is never 

 greater than the value of the money account in 

 year A- — 1 plus the terminal value of the ca- 

 pacity in all of the remaining years (with the 

 lowest prices and smallest catches occurring) 

 minus any fixed cash withdrawals in the rest 

 of the planning period. (All money flows are 

 adjusted for the values of alternative oppor- 

 tunities, income taxes, and depreciation.) This 

 upperbound would be the value of the firm's 

 assets if the worst possible sequence of net 

 revenues occurred — the decisionmaker's final 

 asset position visualizing the worst. 



To reflect the fear of low net revenues, revenue 

 per unit of capacity when the lowest price and 

 yield occurs is assumed to be less than the 

 operating cost per unit of capacity. It is also 

 assumed that per unit prices of capacity are 

 not increasing so rapidly that operating losses 

 per unit may be covered by value appreciation 

 in capacity. (Speculation is never a sure bet.) 

 This implies that the marginal cost of capacity 

 visualizing the worst is positive. Hence, dividing 

 the lower bound for the firm's final asset position 

 by this positive marginal cost, the upper bound 

 for a survivable purchase of capacity in a given 

 year is obtained. This represents the maximum 

 amount of capacity that the decisionmaker can 

 purchase and still insure survival of the firm 

 throughout the rest of the decision period. It 

 depends upon the value of the firm's money 

 account, the amount of capacity owned, and 

 the value of that capacity in the previous year. 

 This upper bound function in year A" is denoted 

 by HkiZk -I, Vk /,^\-/). where at the end 

 of the A- - l^t year z,, -i is the cash balance, 

 yk - / is the units of capacity owned, and .r^ / 

 is the purchase value of the firm's capacity. The 

 firm is in debt if Zk / is negative and has 

 savings if 2* _ ; is positive. 



We will also introduce the following notation 

 now; Si is the units of capacity purchased at 

 the beginning of the i"" year (and used for the 

 first time in year i): t, is the operating costs per 

 unit of capacity in year (; a, is the per unit pur- 

 chase price of capacity before the beginning of 

 the operating season in year i; '-, is the cash with- 



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