The stock of fish in an important North Atlantic fishery is described by the following net augmentation function: F(S)=-1/2(S?4)^2 +3 while the equation describing the harvest as a function of the amount of effort (E) expended by the fishing fleet and the stock (S) of fish is: H = ES. queation: Starting from a world in which fishermen expend no effort in this fishery, find the long-run equilibrium stock of fish if effort rises to E = 1?4. Solution The net augmentation function is as follows: F(S)=-1/2(S/4)2 +3 Whereas Harvest function is as follows: H=ES We need to understand that in finding long run equilibrium, effort is condidered as marginal cost and F(S) is a marginal revenue function. When E = 1/4, harvest function becomes- H = S/4 or S = 4H Equilibrium stock (quantity) is that level at which marginal cost equals marginal revenue. Equating MR and MC -1/2(S/4)2 +3 = 1/4 -S2+96 =8 S = (88)1/2 = 9.38 Hence the long run equilibrium stock of fish is 9 approx..

1. The stock of fish in an important North Atlantic fishery is described by the following net
augmentation function:
F(S)=-1/2(S?4)^2 +3
while the equation describing the harvest as a function of the amount of effort (E)
expended by the fishing fleet and the stock (S) of fish is: H = ES.
queation: Starting from a world in which fishermen expend no effort in this fishery, find the
long-run equilibrium stock of fish if effort rises to E = 1?4.
Solution
The net augmentation function is as follows:
F(S)=-1/2(S/4)2 +3
Whereas Harvest function is as follows:
H=ES
We need to understand that in finding long run equilibrium, effort is condidered as marginal cost
and F(S) is a marginal revenue function.
When E = 1/4, harvest function becomes- H = S/4
or S = 4H
Equilibrium stock (quantity) is that level at which marginal cost equals marginal revenue.
Equating MR and MC
-1/2(S/4)2 +3 = 1/4
-S2+96 =8
S = (88)1/2 = 9.38
Hence the long run equilibrium stock of fish is 9 approx.