FISHERY BULLETIN: VOL. 69, NO. I 



shadow price of the cannery constraint on day 

 7 is shown as $0,069. Note, however, that when 

 an entity 1 fish is released on day 10 that the 

 cannery is no longer at capacity on day 10, 

 hence an entity 3 fish could be caught on day 10 

 if an entity 3 fish was released on day 11. This 

 is an additional contribution to the shadow price 

 for day 7 of 



or 



«'3.10 ~ <^3,11 

 $1,371 - $1,356 



or a profit increase of $0,015. Adding this to 

 the value of catching an earlier entity 1 fish 

 gives $0,054 + $0,015 = $0,069, and this is 

 exactly what is shown for day 7 in Figure 6. 

 Values for days 8 to 10 can be calculated sim- 

 ilarly. 



Next let us consider the run shadow prices 

 (RSP). The increase in value of the objective 

 function corresponding to relaxed run con- 

 straints allowing one more fish of any entity 

 in the catch is the shadow price of that run 

 constraint. If the cannery constraint is not 

 binding, if seasonal run constraints are not used 

 or are not binding, and if egg catch or male 

 escapement consti'aints are not binding, there 

 is no restriction other than the run constraint 

 limiting the catch. Since there is a run con- 

 straint for each entity and day 



RSPij = dj. 



However, if the cannery constraint is effective 

 on day j 



RSPij = Cij - Ci*j 



where entity i* {i*ri) is the fish that must 

 escape to allow the catch of entity i since the 

 cannery is already processing as many fish as 

 possible. And if the egg catch constraint and/ 

 or the male escapement constraint is binding, 

 appropriate numbers of fish must be released 

 when additional fish are caught. As an example 

 of the behavior of the system when the 5 billion 

 egg constraint is used, consider Figure 8. As 

 shown in Figure 8, daily cannery constraints 

 are binding from days 4 to 15, and, in addition. 



I.Male 2-' 

 2. Mole 3- 



3. Femole 2 - 



4, Female 3- 



•Oceon 



Cannery constraints 

 binding these days 



2.00n 



5 10 



Day of season 



Figure 8. — Shadow prices for daily entity run con- 

 straints — an e.xample in which seasonal entity limits are 

 not imposed. 



the egg catch constraint is binding. Although 

 it is not illustrated in the figure, it is essential, 

 in understanding the problem, to realize that the 

 entire escapement satisfying the egg escapement 

 constraint is made up of small (entity 3) females, 

 and that the entire escapement satisfying the 

 male escapement constraint is made up of small 

 (entity 1) males. Also, all fish of all entities 

 are in the catch scheme on days 1 to 3 and 16 

 to 18 (all days on which the cannery constraints 

 are not binding). 



In Figure 8, on days 1 to 3, the cannery con- 

 straints are not binding; and since entity 2 

 escapement is not being used to satisfy any con- 

 straints of any form, the run shadow prices on 

 days 1 to 3 will be equal to the value function 

 (this can be checked with the values listed in 

 Appendix Table 2). In addition, since the male 

 catch constraint is not binding, the run shadow 

 price for entity 1 is also equal to its value func- 



130 



