Externalities 5. (Tragedy of the Commons) Consider a bay where z boats operate in lobster trapping....

 

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Externalities 5. (Tragedy of the Commons) Consider a bay where z boats operate in lobster trapping. Assume that it costs $2000 a month to operate a boat. Suppose further that the total size of the lobster catch (measured in thousands) is f(x) = 10r-r². The price of a lobster is $1. (a) Draw the average and marginal product curves for the number of boats, AP(x) = f(x)/x and MP(x) = df (x)/dx, on the same graph. (b) If there are no restrictions on the number of boats that can operate, how many boats will trap lobsters in the bay. (Hint: Use the zero profit condition.) (e) Now suppose the local village has authority to issue permits which trappers must have to operate in the bay. If the village wants to maximize the size of the lobster catch, how many permits should be issued each month? What it the village wants to maximize welfare? (d) If the village authorities sell monthly permits, at what permit price will the optimal number of permits be purchased by trappers? Externalities 5. (Tragedy of the Commons) Consider a bay where z boats operate in lobster trapping. Assume that it costs $2000 a month to operate a boat. Suppose further that the total size of the lobster catch (measured in thousands) is f(x) = 10r-r². The price of a lobster is $1. (a) Draw the average and marginal product curves for the number of boats, AP(x) = f(x)/x and MP(x) = df (x)/dx, on the same graph. (b) If there are no restrictions on the number of boats that can operate, how many boats will trap lobsters in the bay. (Hint: Use the zero profit condition.) (e) Now suppose the local village has authority to issue permits which trappers must have to operate in the bay. If the village wants to maximize the size of the lobster catch, how many permits should be issued each month? What it the village wants to maximize welfare? (d) If the village authorities sell monthly permits, at what permit price will the optimal number of permits be purchased by trappers?