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Quiz 2: Problem (a)

Quiz 2: Problem (a). 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) < 90 Sell when p < 0.2375 Drill when p  0.2375. Quiz 2: Problems (c), (d), and (e). Random Events

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Quiz 2: Problem (a)

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  1. Quiz 2: Problem (a) Recommendation: Drill for oil.

  2. 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) < 90 Sell when p < 0.2375 Drill when p  0.2375

  3. 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

  4. Quiz 2: Problems (c), (d) and (e) P(FS) = 0.15 + 0.15 = 0.3 P(Oil|FS) = 0.15/0.3 = 0.5 P(US) = 0.10 + 0.60 = 0.7 P(Dry|US) = 0.6/0.7 = 0.86 P(Oil and FS) = 0.15 FS 0.6 US Oil P(Oil and US) = 0.10 0.4 0.25 Dry FS P(Dry and FS) = 0.15 0.2 0.75 US 0.8 P(Dry and US) = 0.60

  5. Oil (0.5) Oil (0.14) Dry (0.5) Dry (0.86) 1 2 3 Decision Tree for Problem f EMV(2) = (0.5)(670-130) = 270 800-100-30=670 Drill -130 FS(0.3) Sell 60 670 Drill US(0.7) -130 Sell 60 EMV(3) = (0.14)(670) + (0.86)(-130) = -18 EMV(1) = (0.7)(60) + (0.3)(270) = 123

  6. 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

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