Quiz 2: Problem (a)

Alternative Oil Dry EMVDrill for oil $700,000 -$100,000 $100,000Sell the land $90,000 $90,000 $90,000Probability 0.25 0.75

Payoff

Recommendation: Drill for oil.

Quiz 2: Problem (b)

• Let p be the probability of oil.

• EMV(Drill) = 700 p – 100 (1-p)

• EMV(Sell) = 90

• Sell when 700 p – 100 (1-p) < 90Sell when p < 0.2375

Drill when p 0.2375

Quiz 2: Problems (c), (d), and (e)

• Random Events– Oil = the land contains oil

– Dry = the land is dry

– FS = favorable sounding

– US = unfavorable sounding

– P(FS|Oil) = 0.6, P(US|Oil) = 0.4

– P(US|Dry) = 0.8, P(FS|Dry) = 0.2

Quiz 2: Problems (c), (d) and (e)

0.25

Dry

0.8

0.2

0.6

P(Oil and FS) = 0.15

P(Oil and US) = 0.10

P(Dry and FS) = 0.15

P(Dry and US) = 0.60

0.75

FS

0.4US

FS

US

Oil

P(FS) = 0.15 + 0.15 = 0.3P(US) = 0.10 + 0.60 = 0.7

P(Oil|FS) = 0.15/0.3 = 0.5P(Dry|US) = 0.6/0.7 = 0.86

Decision Tree for Problem f

1

FS (0.3)

US (0.7)

2Oil (0.5)

Dry (0.5)Drill

Sell

800-100-30=670

-130

60

3Oil (0.14)

Dry (0.86)Drill

Sell

670

-130

EMV(2) = (0.5)(670-130) = 270

EMV(3) = (0.14)(670) + (0.86)(-130) = -18

60

EMV(1) = (0.7)(60) + (0.3)(270) = 123

Optimal Policy

• EMV(No Sounding) = $100,000

• EMV(w/Sounding) = $123,000

• Conclusion:– Pay for the sounding

• If favorable drill

• If unfavorable sell

• EMV = $123,000