By NEAS - 6/28/2005 12:31:11 PM
Microeconomics, Module 19, “Common Property and Public Goods” (Chapter 14)
Homework Assignment
(The attached PDF file has better formatting.)
Suppose many people want to catch fish in a well-stocked lake.
● As the number of fishermen increases, the cost of hiring boats and equipment rises; that is, the marginal cost of fishing rises with the number of fishermen.
● As the number of fishermen increases, the number of fish caught by each person decreases; the marginal value of fishing decreases with the number of fishermen.
The table below shows the marginal cost and value of fishing:
Fishermen Marginal Cost of
Fishing (Per Person) Total Value of
Fish Caught Value per
Fisherman Social Marginal
Benefit
0 – $0 – –
1 $5 $20
2 $6 $36
3 $7 $48
4 $8 $56
5 $9 $60
6 $10 $60
7 $11 $56
8 $12 $48
A. Complete the last two columns of this table. The “value per fisherman” is the average value per fisherman, assuming all fishermen have equal ability to catch fish. For example, the value per fisherman for two fishermen is $36 / 2 = $18.
B. The social marginal benefit is the additional social value of the last fisherman. For example, the social marginal benefit of the second fisherman is $36 – $20 = $16.
C. If the lake is common property, how many fishermen will use it? (Choose the row where the marginal cost to the fisherman in the second column equals the average value of fishing to the fisherman in the fourth column.)
D. How much social gain is created by fishing in the lake? (For the row determined above, use the value of the fish caught minus the product of the number of fishermen and the marginal cost of each fisherman.) You should get an answer of $0, since all gains from common property are dissipated.
Question: The marginal cost includes the value of the fisherman’s time. This example says that the net present value of fishing is zero. That is true for all work; if we include the value of one’s time, the net present value of any occupation should be zero (in a competitive labor market). What is different about common property?
Answer: The cost includes the value of the fisherman’s time but not the opportunity cost of the lake. The lake is a valuable asset. If there were only one fisherman, he would pay $20 – $5 = $15 to use the lake. The lake produces a daily income of $15, which might be worth $50,000 (depending on the opportunity cost of capital, the growth rate of the daily income, and the lifetime of the daily income).
If there were only two fishermen, they would pay $36 – 2 × $6 = $24 to use the lake. The lake produces a daily income of $24, which might be worth $80,000, depending on the opportunity cost of capital, the growth rate of the daily income, and the lifetime of the daily income. These variables depends on the daily depletion of fish from the lake.
Our concern is not the value of fishing as an occupation. If fishing is competitive, fishermen earn a normal wage for their efforts. Our concern is the value of the lake itself. Although the lake is clearly a valuable asset, all its value is dissipated by overuse.
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By NEAS - 8/20/2018 9:34:05 PM
+xResponding to the posts from newjenl, jercox, and sleepyinseattle above, with regards to Question 2 on page 494 in the textbook (the seven dwarves problem): I agree with all of these candidates that the book's solution to part d must be wrong, although I don't exactly agree with any of the candidates' postings either. According to the textbook, the wicked queen will charge each miner 16 nuggets per day to enter Mine A, and 18 nuggets per day to enter Mine B. Clearly, under this fee structure, of the first six dwarves, 2 would choose to enter Mine A and 4 would choose to enter Mine B. The seventh dwarf would then face the choice of paying a fee of 16 nuggets to enter Mine A (which would yield 16 nuggets) or a fee of 18 nuggets to enter Mine B (which would yield 18 nuggets) or to stay home and earn nothing. Since the seventh dwarf has nothing to gain by entering either Mine, I think he would stay home and the wicked queen would only collect six entrance fees totaling 104 nuggets (2 * 16 + 4 * 18). In the best-case scenario for the queen, the seventh dwarf would be Dopey and would choose to pay the 18-nugget fee to work all day collecting 18 nuggets in Mine B, rather than staying home, meaning the queen would collect 104 + 18 = 122 nuggets. That is probably what the book believed would happen. Under the book's solution, the queen gets, at most, 122 nuggets. A better admission fee structure for the queen would be to charge 15 nuggets to enter Mine A and 20 nuggets to enter Mine B. Under this scenario, all seven dwarves would have some incentive to mine, because they would each harvest more nuggets than their admission fee. Three of them would choose to enter Mine A, paying 15 nuggets each to harvest 16 nuggets each. Four of them would choose to enter Mine B, paying 20 nuggets each to harvest 21 nuggets each. Each dwarf goes home at the end of the day with one nugget in his pocket, getting at least some reward for going off to work for a day. Here, the queen collects seven entrance fees totaling 125 nuggets (3 * 15 + 4 * 20). The book's solution clearly does not maximize the wicked queen's profit. I think the solutions to all of question 2 are as follows: a) If entry to the mines is free, 2 miners work in A and 5 miners work in B. b) At social optimum, 3 miners work in A and 4 miners work in B. c) One way to bring about that social optimum would be to charge anywhere between 3 and 6 nuggets to work in Mine B, while still letting access to Mine A be free of charge. d) The wicked queen would charge 15 nuggets to enter Mine A and 20 nuggets to enter Mine B. |
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