There are N fishers in a community. Some of them fish in the ocean. The ocean is
ID: 3143646 • Letter: T
Question
There are N fishers in a community. Some of them fish in the ocean. The ocean is so large that each fisher can catch w fish no matter how many fishers go to sea. Some of the fishers fish in a lake. (Lake fish and ocean fish are perfect substitutes in consumption.) If there are x fishers on the lake, each of them catches x^-1/2 fish (i.e., x^1/2 fish are caught in total and each worker catches the same number). (a) If each fisher is free to choose whether to go to the ocean or the lake and no one will go where he expects to catch fewer fish, how many fishers will go to the lake, how many to the ocean, and what will be the average catch? (b) If the government restricts access to the lake, how many fishers should it allow on the lake to maximize the total catch in the community? (c) Assume the government charges for a license to fish in the lake and sells as many licenses as fishers want to buy. What size lake fishing license supports this equilibrium? Assume the revenue from the licenses goes completely to consumers who do not fish. Are the fishers better off, worse off, or the same after the introduction of the optimal licenses, as opposed to no government intervention? Might your answer be different with a different technology on the ocean? Explain. (d) Now assume that all the fish are sold and the demand for fish is: Q = A - BP Compare the price of fish in the free access and efficient allocations. Now assume that ocean fish and lake fish are not perfect substitutes. The demand for ocean fish is such that each fish is worth $2. The demand for lake fish is Q_L = A' - B'P_L How many lake fishers are there in free access equilibrium? If a positive license fee is charged for fishing in the lake, does the price of lake fish go up or down? What makes this case different from that above?Explanation / Answer
(a)
Total fishers = N
Fishers going to lake = x, they get x-1/2
Fishers going to ocean = N - x, they get w fishes
if x > 1, each fisher get less than 1 fish which means no fish.
so if w > 0, at max only 1 fisher will go to lake
x : no . of fishers going to lake
so x = 1 if w = 1
and x = 0 if w > 1
(b)
total catch = catch from ocean + catch from lake
using notation of the above question part
total catch = w (N-x) + x1/2
total catch (T) = wN - wx + x1/2
differentiate it w.r.t. to x to find out local maxima and minima (first derivative is 0)
dT/dx = 0 - w + 1/2 x-1/2
x = 1/ (4w2)
since w is an integer, x < 1 always.
so all the fishers are going to ocean.
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