This question illustrates the argument on p.114 of the book. A and B own neighboring properties. Beneath their properties is a common well that contains 200 units of oil. The cost to A of extracting oil from the well in period t depends on the number of units of oil in the well at the beginning of the period t, ut, and the number of units of oil A extracts in period t, xAt ; specifically, the average cost of extraction for A per unit in period t is xAt /ut. The analogous cost function for B is xBt/ut. The market price of a barrel of oil is 1, there are two periods (t = 1, 2), and the discount rate is zero. The oil is a common property resource. a) (2) Suppose that A and B "unitize" and cooperatively decide how much oil to extract, and split the profit between them. The jointly profit-maximizing policy is that each extracts 50 units of oil from her well in each of the first two periods, after which the well is dry. How much discounted profit will A and B each make? b) (2) Suppose instead that A and B do not cooperate in deciding how much oil to extract. Each will extract 75 units of oil from her well in the first period, and 25 units in the second. How much discounted profit will A and B each make? c) (3) What accounts for the difference in the two solutions? d) (3) What economic principle does the example illustrate about "the commons"?
This question illustrates the argument on p.114 of the book.
A and B own neighboring properties. Beneath their properties is a common well that contains 200 units of oil. The cost to A of extracting oil from the well in period t depends on the number of units of oil in the well at the beginning of the period t, ut, and the number of units of oil A extracts in period t, xAt ; specifically, the average cost of extraction for A per unit in period t is xAt /ut. The analogous cost function for B is xBt/ut. The market price of a barrel of oil is 1, there are two periods (t = 1, 2), and the discount rate is zero. The oil is a common property resource.
a) (2) Suppose that A and B "unitize" and cooperatively decide how much oil to extract, and split the profit between them. The jointly profit-maximizing policy is that each extracts 50 units of oil from her well in each of the first two periods, after which the well is dry. How much discounted profit will A and B each make?
b) (2) Suppose instead that A and B do not cooperate in deciding how much oil to extract. Each will extract 75 units of oil from her well in the first period, and 25 units in the second. How much discounted profit will A and B each make?
c) (3) What accounts for the difference in the two solutions?
d) (3) What economic principle does the example illustrate about "the commons"?
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