The fishermen on the Sea of Nowhere have to search for schools of fish. When a...

 

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The fishermen on the Sea of Nowhere have to search for schools of fish. When a fisherman finds a school of fish he spends h hours fishing and gets the square root of h units of fish (h0.5). The fishermen compete for fish. When there are n fishermen, it takes each fisherman n² hours to find a new school. A fisherman can earn sufficient revenue to cover his costs if he gets 1 unit of fish every 16 hours. a. Find the average cost in time per unit of fish if a fisherman gets h0.5 units of fish from each patch. This will be an equation in terms of h and n. b. How much time will an efficient fisherman spend fishing each school when there are n fishermen? (Hint: Minimize average cost from (a). Your answer will be h as some function of n.) c. Since there is free entry into this fishery, the equilibrium number of fishermen is the maximum number of efficient fishermen who can survive. How many is this? (Hint: This will be a whole number. If you are getting a partial fisherman, you have an error.) The fishermen on the Sea of Nowhere have to search for schools of fish. When a fisherman finds a school of fish he spends h hours fishing and gets the square root of h units of fish (h0.5). The fishermen compete for fish. When there are n fishermen, it takes each fisherman n² hours to find a new school. A fisherman can earn sufficient revenue to cover his costs if he gets 1 unit of fish every 16 hours. a. Find the average cost in time per unit of fish if a fisherman gets h0.5 units of fish from each patch. This will be an equation in terms of h and n. b. How much time will an efficient fisherman spend fishing each school when there are n fishermen? (Hint: Minimize average cost from (a). Your answer will be h as some function of n.) c. Since there is free entry into this fishery, the equilibrium number of fishermen is the maximum number of efficient fishermen who can survive. How many is this? (Hint: This will be a whole number. If you are getting a partial fisherman, you have an error.)