Question

Residents of the Michigan shoreline villages of Empire, Glen Arbor and Leland were surprised as they awoke to see the Lake Michigan beach covered with the latest Great Lakes invasive species to threaten the shores, lobsters. The town councils have decided to issue permits to trap lobsters and they are trying to determine how many permits to issue.

The economics of the situation is:

* It costs $2,000 a month to operate a lobster boat

* If there are x boats operating the shoreline, the total revenue from the lobster catch per month will be f(x) = $1,000(10x - x2).

a) In a graph, plot the curves for the average revenue, AR(x)=f(x)/x, and the marginal revenue, MR(x)=10,000 - 2,000x. In the same graph, plot the line indicating the cost of operating the boat.

b) If the permits are free of charge, how many boats will trap lobsters in the Michigan shoreline?

c) What number of boats maximizes total profits?

d) If the villages want to restrict the number of boats to the number that maximizes total profits, how much should they charge per month for a lobstering permit?

Note: no calculus.

Answer 1

We have total cost function C = 2000x, total revenue function = 10000x - 1000x^2. Marginal revenue function = 10000 - 2000x and AR = 10000 - 1000x.

a) Graph is plotted below

b) If the permits are free of charge,there will be 8 boats that trap lobsters in the Michigan shoreline (AR = MC)

c) A total of 4 boats will maximize total profits (MR = MC)

d) If the villages want to restrict the number of boats to the number that maximizes total profits, For a permit, a chrage should be large enough to restric number of boats to 4, the permit should make the profit zero for the permit holders, This can be done when permit charge is equal to profit per boad which is currently $4000. This should be the permit fee.