Question

An oil company has some land that is reported to possibly contain oil. The company classifies such land into four categories by the total number of barrels that are expected to be obtained from the well, a 350,000 barrel well, 100,000 barrel well, 10,000 barrel well, and a dry well. The company is faced with deciding whether to drill for oil, to unconditionally lease the land, or to conditionally lease the land at a rate depending upon oil strike. The cost of drilling the well is $150,000 if it is a producing well and the cost of drilling is $100,000 if it is a dry well. For producing well, the profit per barrel of oil is $1.50, after deduction of processing and all other costs except drilling costs.

Under the unconditional lease agreement, the company receives $30,000 for the land whereas for the conditional lease agreement the company receives 50 cents for each barrel of oil extracted if it is a 350,000 or 100,000 barrel oil strike and nothing if otherwise.

Which alternative should be selected based on the following criteria?

     a) LaPlace

     b) Maximax

     c) Maximin

     d) Hurwicz with a = 0.3

     e) MinMax with regret

Answer 1

Construct the payoff table as follows

	350000 barrel well	100000 barrel well	10000 barrel well	Dry well
Drill	375,000	0	-135,000	-100,000
Unconditionally lease	30,000	30,000	30,000	30,000
Conditionally lease	175,000	50,000	0	0

Payoff for Drill, if it is a 350000 barrel oil well = -150000 + 1.5*350000 = $ 375,000

Payoff for Drill, if it is a 100000 barrel oil well = -150000 + 1.5*100000 = $ 0

Payoff for Drill, if it is a 10000 barrel oil well = -150000 + 1.5*10000 = $ -135,000

Payoff for Drill, if it is a Dry well = -100000

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Payoff for Unconditionally lease, if it is a 350000 barrel oil well = $ 30,000

Payoff for Unconditionally lease, if it is a 100000 barrel oil well = $ 30,000

Payoff for Unconditionally lease, if it is a 10000 barrel oil well = $ 30,000

Payoff for Unconditionally lease, if it is a Dry well = $ 30,000

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Payoff for Conditionally lease, if it is a 350000 barrel oil well = 350,000*0.5 = $ 175,000

Payoff for Conditionally lease, if it is a 100000 barrel oil well = 100,000*0.5 = $ 50,000

Payoff for Conditionally lease, if it is a 10000 barrel oil well = $ 0

Payoff for Conditionally lease, if it is a Dry well = $ 0

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