Question

2. Fisheries: Logistic Growth G(S), Y SA SB SC SD SE Fish Stock, S Consider a fishery with annual growth as shown by the curved line in the figure. Suppose the annual catch in the fishery every year is Y1. For each of the five possible starting stock levels, indicate what the fish stock level would be in the long run (that is, after many periods) if there were a continued annual catch of Y1 A) If the initial fish stock is SA, show what the fish stock would be in the long run. B) If the initial fish stock is SB, show what the fish stock would be in the long run. C) If the initial fish stock is Sc, show what the fish stock would be in the long run. D) If the initial fish stock is Sp, show what the fish stock would be in the long run E) If the initial fish stock is Se, show what the fish stock would be in the long run.

Answer 1

For the initial stock Sa if we increase the stock then annual stock of fish will increase that will continue increasing until the stock is equal with the annual catch of fish which is Y1 thus in long run the fish stock will be Sb

For initial Sb as the annual amount of catch and annual stock of fish is equal in long run it will be at the same point.

Similar as Sb, at Sc the fishery owner will stock the highest amount fish annually thus he will try not to deviate from that point,

For initial point Sd as again the amount of stock and catch fish annually is equal in long run the stock point will be Sd

for initial point Se as if we increase stock it will be less thus revenue will be less thus the fishery owner will try to decrease the amount of stock annually thus in long it will go back to the point Sd.