FISHERY BULLETIN: VOL. 69, NO. 1 



constraint is not binding, i.e., there are entity 

 3 females available to be caught. The formula 

 indicates that allowing the catch of one more 

 egg essentially allows the catch of 1/3,700 of 

 an entity 3 female which requires the escape- 

 ment of 1/3,700 of some other fish since the 

 cannery constraint is binding. The fish to be 

 included in the escapement is, of course, the low- 

 valued entity 1 male. 



If the cannery constraint on day j is binding, 

 but there is a day when the entity 4 run con- 

 sti'aint is not binding, and since the value of a 

 large female per egg is greater than the value 

 of a small female per egg, the value of allowing 

 the catch of an additional egg is 



ESP= (C4J -C|j)/4,384 



where day .;" is a day on which the entity 4 run 

 constraint is not binding. 



If the cannery constraint is not binding on 

 day j then catching additional females does not 

 require the escapement of an equal number of 

 males, or, in other words, the addition of the 

 marginal fish does not require the release of 

 a fish extant in the catch. If, however, all the 

 entity 4 run constraints are binding through 

 the season, then 



ESP = C3,,/ 3,700 



where day ; is a day on which the entity 3 run 

 constraint is not binding. Or, if an entity 4 run 

 constraint is not binding on day j and again 

 since the value of a large female is greater than 

 that of a small female, 



ESP=C4j4M4- 



The next shadow price that we will evaluate is 

 the increase in value of the ability to process 

 an additional or marginal fish. The imputed 

 value of processing a marginal fish is called 

 the shadow price of the cannery constraint 

 (CSP), and we must remember that this mar- 

 ginal fish only has an imputed positive value 

 if the cannery constraint is binding. In other 

 words, we can impute a value to an additional 

 unit of cannery capacity. Following the format 



above, the shadow prices for the cannery con- 

 straint can be outlined. For emphasis, we re- 

 peat again that if the cannery constraint is not 

 binding, indicating that the value of this catch 

 scheme is not being limited by this constraint, 

 then the shadow price associated with the can- 

 nery constraint is zero. If the cannery con- 

 straint is binding, shadow pi'ices associated with 

 the cannery constraint, given which other con- 

 straints are effective, can be determined. 



The objective function will be increased by 

 an amount equal to the value of the additional 

 fish which is included in the new catch scheme 

 (the scheme arising from relaxing the cannery 

 constraint), and hence the most valuable fish 

 will be caught. If run constraints are not bind- 

 ing, the shadow price is 



CSPj = C2j 



since the large males are the most valuable. 

 As the run constraints become binding for the 

 more valuable entities, the shadow price of the 

 cannery constraints is equal to the value of the 

 most valuable entity available. 



If, for example, the egg catch constraint is 

 binding as well as the entity 2 run constraint, 

 the shadow price of the cannery constraint is 



CSPj =c4j 



/ 4,384 

 y 3,700 



C3, 



The modification of the equation assures that 

 enough eggs will escape (via entity 3 female) to 

 enable the catch of the more valuable entity 4 

 female. 



To emphasize the effect of reduced escape- 

 ments and concomitant binding egg catch con- 

 straints, we employed the 1960 run model but 

 dropped equation (13) and used an effective 

 escapement of 5 billion eggs in equation (10). 

 If the egg catch constraint is binding as well 

 as entity 4 run constraints, the only fish avail- 

 able for catching are the entity 1 (small males), 

 since no more females can be caught without 

 violating the egg catch constraint. Hence 



CSPj = c|j. 



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