Nov 20 2009

Another Mankiw problem for the motivated Micro student!

Greg Mankiw’s Blog: Take Out Your Pencils 2

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?)

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).

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?

About the author:  Jason Welker teaches International Baccalaureate and Advanced Placement Economics at Zurich International School in Switzerland. In addition to publishing various online resources for economics students and teachers, Jason developed the online version of the Economics course for the IB and is has authored two Economics textbooks: Pearson Baccalaureate’s Economics for the IB Diploma and REA’s AP Macroeconomics Crash Course. Jason is a native of the Pacific Northwest of the United States, and is a passionate adventurer, who considers himself a skier / mountain biker who teaches Economics in his free time. He and his wife keep a ski chalet in the mountains of Northern Idaho, which now that they live in the Swiss Alps gets far too little use. Read more posts by this author

2 responses so far

2 Responses to “Another Mankiw problem for the motivated Micro student!”

  1. Spencer Coeon 01 Dec 2009 at 6:04 am

    Okay Jason, I'll bite (couldn't resist the pun):

    A. I believe we are looking for the law of diminishing marginal productivity. More people using the same "land" to produce fish leads to lower and lower marginal catches. Additionally, I can't ignore that people who fish often claim that more fishing pressure leads to more educated fish – they get harder to catch. As for the fish farmers, I assumed that the farmers each have their own pond, so no, they do not face the same diminishing marginal productivity as they are increasing more than just labor (each new farmer (labor) creates a new pond (land/capital)).

    B. Under the Freedom Party's policy we would have 4 people on the lake and 1 on the farm for a total of 10 fish. People will fish wherever they can get more fish, it is only at 4 on the lake and 1 on the farm that there is no incentive to change fishing methods.

    C. Assuming that this is sustainable, the Efficiency party would like to see 2 people on the lake and 3 on the farms. This would result in 14 fish.

    D. The efficiency party would advocate a tax of 2 fish. If implemented 2 people would fish on the lake and the rest would go to the farms.

    E. The efficiency party's tax and redistribution to all would result in everyone having 2.8 fish. In theory the entire community would benefit from more fish (unless we are overfishing the lake) and the fish farmers would be much better off. The lake fishers would perceive themselves as being worse off as they caught 4 fish each but only ended up with 2.8 fish. The efficiency party would argue that without the tax there would have been so many fishermen on the lake that each would have only caught 2 fish. Additionally, the question of sustainability is the same in either situation since in each case 8 fish are being removed from the lake.

    Although this question leads us to believe that the tax is a good thing I discussed with my classes the fact that there is a cost in taxation and redistribution so the end result of 2.8 would not occur although even 2.6 fish (or some other amount) is a better situation for the community.

    In the short-run also believe that there would be a disincentive for the lake fishers to stay on the lake EVEN if we assume that catching 4 fish on the lake has the same risk and entails the same amount of work as farming 2 fish. Lake fishers will simply come to believe that they are subsidizing the fish farmers and will believe that they will benefit more by farming fish. I believe that a lake fisher will switch to farming where he can gain 2.8 fish for farming 2 fish instead of working to catch 4 fish and having only 2.8 fish. Of course, once 1 leaves the lake the other will gain causing a farmer to switch back to the lake.

    Some students suggested saving some trouble by taxing 1.2 fish and only redistributing to the farmers but other students were quick to point out the flaw in this.

  2. Jason Welkeron 01 Dec 2009 at 7:03 am


    GREAT response! I am glad someone finally posted a reply to this one! I got the same answers as you did for A through E, so that makes me feel good. I like your analysis of the tax, however.

    I'd throw this thought out there as well. I am from the Pacific Northwest, where the issue of farm raised fish versus wild caught fish is a major one. Your discussion of the non-economic motivations of lake fisherman and the possibility that they'll desire to switch to farming due to the "unfairness" of the 50% tax on and re-distribution of their catch is thought provoking, indeed. I do wonder how wild fisherman weigh the decision whether or not to remain in the business when they consider the benefits (and costs) of switching to a much less labor intensive alternative, farming fish, which basically requires one to occasionally visit an area of a lake cordoned off by nets, apply large amounts of food and anti-biotics and other non-organic compounds to the pools of fish which are living in extremely close quarters and experiencing stresses they would never encounter in nature, all the while receiving subsidies from the government to keep them in operation and out of the wild fishing business.

    I would posit that the wild fisherman will want to remain on the lake because once one switches to farming, two things happen. 1) he pays no tax, rather receives a subsidy, and 2) he gets less fish each week, since the community's total catch goes down. Non-economically speaking, he abandons a demanding yet rewarding career as a "wild" fisherman for the rather dull and benign career as a fish farmer dependent on state handouts to stay in business.

    Once we take into account the negative externalities of fish farming on the ecosystem of the lake, it could be argued that too many fish farmers will create spillover costs on other users of the water resource, which may mean taxes on fish farming should too many switch to this method. Combine that with the decline in weekly earnings and the ever increasing incentive is to move back to catching wild fish, despite the tax!

    For the record, I only eat wild salmon when home in the summers. Farmed fish creates several harmful impacts on the ecosystems of the Pacific Northwest waters. Yeah, it's cheaper, but nothing's better tasting and more satisfying than a wild Sockeye or Chinook caught by the sweat and blood of man.

    Thanks for the insights!