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Question 5. (25 points) Consider a dynamic model with age-structured fisheries. In this
model there are two types of fish; adults and juveniles (for example, salmon and caviar).
Let Jt represent the biomass of juveniles at time t. Let At represent the biomass of adults
at time t. The biomass of juveniles in period t + 1 depends on the escapement of adults in
period t according to the net growth function F(St), where escapement is St = At - YA, and
YA represents the catch of adults at time t. The biomass of adults in period t + 1 depends
on juvenile natural mortality m and the harvest of juveniles Y,B. In summary, the dynamics
of the two species are determined by:
At + 1 = At + FLA) -Yt
J+ +1 = F(S. )
Se = At - Yet
Att1 = Jt - mat - Y
with 0 < m < 1 .
St
Suppose the two types of fish are harvested with linear harvesting rules such that a propor-
tion of the biomass of each type is harvested at each time period:
YA = aAt
with 0 < a < 1 ,
YJ = BJt with 0 < B < 1.
Assume F(St) = St, y = 0.5, m = 0.1, a = 0.5, and B = 0.1.
a. What is the steady state biomass of Adults, and Juveniles?
b. What is the steady state catch of Adults, and Juveniles?
A traditional management policy is for fisheries to adopt fish size restrictions. Suppose that
harvest of Juveniles is prohibited (and fully enforced) under size restriction regulation.
c. What is the steady state biomass of Adults and Juveniles under size restrictions?
d. What is the steady state catch of Adults and Juveniles under size restrictions?
e. Suppose the fishery's objective is to maximize steady state revenues. Market price for
adults is PA = 10 and for juveniles is Py = 20. Would the fishery have incentives to lobby
against the size restriction regulation?

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