FISHERY BULLETIN: VOL. 69, NO. 1 



the release of the entity 3 is on a day which a 

 male entity is available, that entity can be caught 

 without breaking the cannery constraint, e.g., 



(Note that day 7 is the first day on which there 

 is a male entity not already in the catch scheme, 

 and hence, the price differential is smallest.) 



/?SP3,8, = $ 1 .404 

 = $o'.002, 



$1,307 - $1,419 + $1,324 



which is that value shown in Figure 8. 



Run shadow price for entity 4 days 4 to 15 

 can be calculated by releasing and catching the 

 fractional parts 4,384/3,700 of entities 3 and 1 

 as requii-ed to maintain cannery and egg catch 

 constraints, in a manner similar to that for days 

 1 to 3. The run shadow prices for the male 

 entities for days 16 to 18 (those days after the 

 cannery constraints are no longer binding) are 

 simply equal to the value of those entity-days, 

 since they are not involved in satisfying any 

 constraints of any form. The run shadow prices 

 for the female entities on these days are a little 

 more difficult to arrive at, since as they are 

 caught, an equal number of eggs must be re- 

 leased, resulting in a slack cannery constraint 

 which can be filled by catching additional male 

 entities when available. 



Consider, in contrast. Figure 9, where the run 

 shadow prices are shown for a case in which we 

 used the actual escapement for the 1960 run in 

 constraint equation (13). The seasonal limit 

 constraints are binding for all entities in this 

 example. It follows that in every case when cal- 

 culating a run shadow price for an entity day, 

 the inclusion of an additional unit of any entity 

 on that day implies that a unit of that entity 

 must escape on some other day of the season to 

 maintain the equality of the seasonal limit con- 

 straint for that entity. 



In Figure 9, shadow prices are plotted for the 

 daily run constraints for the particular example 

 in which seasonal limits were imposed to achieve 

 the actual escapements of 1960. Neither the 

 egg catch constraint nor the male catch con- 



l.Male 2- 



2. Mole 3- 



3. Female 2 - 



4. Femole 3- 



• Ocean 



Cannery constraints 

 binding these days 



0.20 







5 10 



Day of season 



Figure 9. — Shadow prices for daily entity run con- 

 straints — an example in which seasonal entity limits are 

 imposed. 



straint was binding; the seasonal limit con- 

 straint was binding for each entity. Cannery 

 constraints were binding from days 4 to 10, as 

 indicated on the figure. In calculating the run 

 shadow price for any entity on any day, note that 

 whenever an additional fish is included in the 

 catch scheme, a fish of that same entity must 

 be eliminated from the catch scheme on some 

 other day in order to maintain a valid seasonal 

 limit constraint for that entity. Thus, for entity 

 1 days 1 to 3, the run shadow price can be cal- 

 culated as the value of a fish included on the 

 day being considered minus the value of the low- 

 est valued fish of entity 1 in the catch scheme 

 which must be released to keep the constraints 



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