1. (10) Inefficiency of Common Pool Resource Use. A and B own neighboring proper
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Question
1. (10) Inefficiency of Common Pool Resource Use.
A and B own neighboring properties. Beneath their properties is a well that contains 100 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 he 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) 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 25 units of oil from his well in each of the first two periods, after which the well is dry. How much profit will A and B each make?
b) Suppose instead that A and B do not cooperate in deciding how much oil to extract. Each will extract 37.5 units of oil from his well in the first period, and 12.5 units in the second. How much profit will A and B each make?
c)What accounts for the difference in the two solutions? d) (3) What economic principle does the example illustrate about "the commons"?
Explanation / Answer
According to the information presented, we are facing a typical example about the Tragedy of the Commons where individuals most cooperate among them in the shared resource system if they want to obtain a profitable situation.
A. In a situation where A and B decide to cooperate:
25 units of oil from a well in each period
Sales in period t1 = 25 units * 1$ per unit = 25 $
Cost of Extraction per unit in period t1 = 25/100 = 0.25$
Cost of Extraction in period t1 = 0.25$ * 25 units = 6.25 $
Profit in period t1 = 25 – 6,25 = 18.75 $
Sales in period t2 = 25 units * 1$ per unit = 25 $
Cost of Extraction per unit in period t2 = 25/100 = 0.25$
Cost of Extraction in period t2 = 0.25$ * 25 units = 6.25 $
Profit in period t2 = 25 – 6.25 = 18.75 $
Total Profit A and B each make = 18.75 + 18.75 = 37.50 $
B. In a situation where A and B decide do not cooperate:
37.5 units of oil from a well in period 1
12.5 units of oil from a well in period 2
Sales in period t1 = 37.5 units * 1$ per unit = 37.50 $
Cost of Extraction per unit in period t1 = 37.5/100 = 0.375$
Cost of Extraction in period t1 = 0.375$ * 37.5 units = 14.06 $
Profit in period t1 = 37.50 – 14.06 = 23.44 $
Sales in period t2 = 12.5 units * 1$ per unit = 12.50 $
Cost of Extraction per unit in period t2 = 12.50/100 = 0,125$
Cost of Extraction in period t2 = 0,125$ * 12.50 units = 1.56 $
Profit in period t2 = 12.50 – 1.56 = 10.94 $
Total Profit A and B each make = 23.44 + 10.94 = 34.38 $
C. The difference presented in the two solutions is an example of what happens in a common pool system when individuals decide to act for their own benefit and not cooperate, the result is that they get a lower profit than they would have obtained if they have decided to cooperate. This example illustrates the important economic principle about the Tragedy of the Commons.
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