4. * Two companies each own property (and mineral rights) in an oil field. Each firm therefore has the legal right to drill for oil on its land and take out as much oil as it can. The problem, of course, is that one company's actions affect how much oil the other can produce. The following matrix represents how each of these companies view the situation. The terms outside the matrix represent oil output by each firm (low, medium, or high), while the numbers in each cell show the present value of all oil to be extracted by each company, given the 2 extraction policies. The first number represents the value to Company A and the second number represents the value to Company B. As an example, if Company A pumps at a "low” rate, and Company B pumps at a "low" rate, then the value to Company A of all the oil it expects to take over the life of the field is $100 while the value to Company B of its oil is $8. Company A's Extraction Rate Low Medium High Company B's Extraction Rate Low 100, 8 125,5 120, 3 Medium 80, 15 110, 10 115, 8 High 50, 30 55,22 60, 20 a. What extraction rates maximize the total value of the oil field? b. Does the set of extraction rates of part (a) represent a stable situation? Explain. C. Is there a dominant strategy (extraction rate) for either or both players? Explain. d. Is there a Nash equilibrium set of extraction rates? If so, does it maximize the total value of the oil field? e. Is there a mutually beneficial exchange inherent in this matrix-one that could solve the problem these 2 companies face? If Company A were put purchase Company B's oil rights, how much would it have to pay? Is this a feasible transaction?
4. * Two companies each own property (and mineral rights) in an oil field. Each firm therefore has the legal right to drill for oil on its land and take out as much oil as it can. The problem, of course, is that one company's actions affect how much oil the other can produce. The following matrix represents how each of these companies view the situation. The terms outside the matrix represent oil output by each firm (low, medium, or high), while the numbers in each cell show the present value of all oil to be extracted by each company, given the 2 extraction policies. The first number represents the value to Company A and the second number represents the value to Company B. As an example, if Company A pumps at a "low” rate, and Company B pumps at a "low" rate, then the value to Company A of all the oil it expects to take over the life of the field is $100 while the value to Company B of its oil is $8. Company A's Extraction Rate Low Medium High Company B's Extraction Rate Low 100, 8 125,5 120, 3 Medium 80, 15 110, 10 115, 8 High 50, 30 55,22 60, 20 a. What extraction rates maximize the total value of the oil field? b. Does the set of extraction rates of part (a) represent a stable situation? Explain. C. Is there a dominant strategy (extraction rate) for either or both players? Explain. d. Is there a Nash equilibrium set of extraction rates? If so, does it maximize the total value of the oil field? e. Is there a mutually beneficial exchange inherent in this matrix-one that could solve the problem these 2 companies face? If Company A were put purchase Company B's oil rights, how much would it have to pay? Is this a feasible transaction?
Chapter13: General Equilibrium And Welfare
Section: Chapter Questions
Problem 13.12P
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Transcribed Image Text:4.
* Two companies each own property (and mineral rights) in an
oil field. Each firm therefore has the legal right to drill for
oil on its land and take out as much oil as it can. The
problem, of course, is that one company's actions affect how
much oil the other can produce. The following matrix
represents how each of these companies view the situation.
The terms outside the matrix represent oil output by each
firm (low, medium, or high), while the numbers in each cell
show the present value of all oil to be extracted by each
company, given the 2 extraction policies. The first number
represents the value to Company A and the second number
represents the value to Company B. As an example, if
Company A pumps at a "low" rate, and Company B pumps at
a “low” rate, then the value to Company A of all the oil it
expects to take over the life of the field is $100 while the
value to Company B of its oil is $8.
Company A's
Extraction Rate
Low
Medium
High
a.
Company B's Extraction Rate
Low
High
50, 30
55, 22
60, 20
100, 8
125, 5
120, 3
Medium
80, 15
110, 10
115, 8
What extraction rates maximize the total value of the oil
field?
b. Does the set of extraction rates of part (a) represent a stable
situation? Explain.
C.
Is there a dominant strategy (extraction rate) for either or
both players? Explain.
d. Is there a Nash equilibrium set of extraction rates? If so,
does it maximize the total value of the oil field?
e. Is there a mutually beneficial exchange inherent in this
matrix-one that could solve the problem these 2
companies face? If Company A were put purchase
Company B's oil rights, how much would it have to pay?
Is this a feasible transaction?
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