Another Mankiw problem for the motivated Micro student! | Welker's Wikinomics Blog - 2 views
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Harvard’s Greg Mankiw just keep them coming! Here’s another micro problem from the esteemed professor and textbook author’s blog. Several readers enjoyed challenging themselves with his last Micro problem, so I will re-publish Mankiw’s test question here to see if people can solve it in the comment section on this blog (sorry Professor Mankiw, you have comments turned off on your blog, so how are your readers to know if they have solved it correctly?)
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The town of Wiknam has 5 residents whose only activity is producing and consuming fish. They produce fish in two ways. Each person who works on a fish farm raises 2 fish per day. Each person who goes fishing in the town lake catches X fish per day. X depends on N, the number of residents fishing in the lake. In particular, X = 6 – N. Each resident is attracted to the job that pays more fish. a. Why do you suppose that X, the productivity of each fisherman, falls as N, the number of fishermen, rises? What economic term would you use to describe the fish in the town lake? Would the same description apply to the fish from the farms? Explain. b. The town’s Freedom Party thinks every individual should have the right to choose between fishing in the lake and farming without government interference. Under its policy, how many of the residents would fish in the lake and how many would work on fish farms? How many fish are produced? c. The town’s Efficiency Party thinks Wiknam should produce as many fish as it can. To achieve this goal, how many of the residents should fish in the lake and how many should work on the farms? (Hint: Create a table that shows the number of fish produced—on farms, from the lake, and in total—for each N from 0 to 5.) d. The Efficiency Party proposes achieving its goal by taxing each person fishing in the lake by an amount equal to T fish per day and distributing the proceeds equally among all Wiknam residents. Calculate the value of T that would yield the outcome you derived in part (c).
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e. Compared with the Freedom Party’s hands-off policy, who benefits and who loses from the imposition of the Efficiency Party’s fishing tax?
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Okay, this time I want to get in on the action before all you smart people get this one right on your first try again! I will offer my answers, but withhold the explanations for further discussion once other people have had a chance to chime in. a) Productivity of additional fishermen falls on the lake due to the law of diminishing marginal returns. Fish farmers would not experience diminishing returns, since each farmer is given access to additional land (or in this case water) and capital, assuming each farmer has his own farm. On the lake, labor is the only variable resource. On farms, land and capital vary with labor, assuring marginal product remains constant as additional residents get into fish farming b) Without any government interference, 1 resident will farm fish, and four will fish on the lake. c) To maximize town's total output of fish, only two residents should fish on the lake, and three should farm fish. d) To yield the maximum output of fish for the town, the town should tax lake fisherman by 2 fish. T=2. e) The hands off policy would have yielded 2 fish per resident per day. The fishing tax will ultimately yield each resident 2.8 fish per day. Therefore everyone benefits. The two lake fisherman give up half their daily catch to the government, but get part of it back through the re-distributive plan. Who else has their own answers, or explanations of MY answers!!??
