Consider an oil-wildcatting problem. A decision maker has mineral rights on a pi
ID: 455507 • Letter: C
Question
Consider an oil-wildcatting problem. A decision maker has mineral rights on a piece of land that he believes may have oil underground. There is a 30% chance that the decision maker will strike oil if he drills. If he drills and strikes oil, then the net payoff is $180,000. If he drills and does not strike oil, then there will be a $10,000 loss due to the sunk cost. The alternative is not to drill at all, in which case the decision maker's net payoff is $0.
Before the decision maker drill he might consult a geologist who can assess the promise of the piece of land. The geologist can tell the decision maker whether the decision maker's prospects are "good" or "poor". But she (the geologist) is not a perfect predictor. If there is oil, the conditional probability is 0.9 that she will say good. If there is no oil, the conditional probability is 0.85 that she will say poor.
What is the maximum amount that the decision maker (assume he is rational) is willing to pay the geologist for her information? (Calculate EVSI.)
Explanation / Answer
EVSI= Expected Best Value with Sample information - Expected Best Value without Sample Information
Expected Best Value without Sample Information = Max ((0.3 X180000-0.7 X 10000),0) = 47000
Geologist now enters the picture. We will calculate posterior probabilities using bayes formula
P(oil is present/geologist said good)= P(geologist said good/ oil is present)P(oil is present)/[ (P(geologist said good/ oil is present)P(oil is present) +P(geologist said good/ oil is not present)P(oil is not present)
=0.9 X 0.3/(0.9 X 0.3 +0.1 X 0.7)
=0.27/(0.27+0.07) =0.79
Using similar fomulas
P(oil is not present/geologist said good) =0.21
P(oil is not present/geologist said not good)= (0.7 X0.85)/ (0.7X 0.85+ 0.3 X 0.15) =0.93
P(oil is present/geologist said not good)= 0.07
P (geologist said good) =(0.9 X 0.3 + 0.15 X 0.7)= 0.375
P(geologist said not good) =0.625
Expected value of striking oil if geologist said good = 0.79 X180000- 0.21 X10000 = 140,100
Expected value of striking oil if geologist said not good = (0.07 X180000- 0.92 X10000) =3,400
Expected value of drilling after consultation = 0.375(140100)+0.625(3400) = 54662.5
Expected value of not drilling after consultation =0
Expected Best value with Sample Information =Max( 54662.5,0) =54662.5
EVSI= Expected Best Value with Sample information - Expected Best Value without Sample Information
= 54662.5 -47000 = 7662.5