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?