Mrs Moore is a agriculturalist and would like to drill for water on her farm. She needs water for irrigation and estimates the benefits of having a successful borehole as $2.0m. However, there is only a 10% chance that she will strike water if she drills and the cost of drilling is $100 000. The alternative is not to drill at all, in which case the benefit will be zero.   Draw a decision tree to represent the problem. Should Mrs Moore go ahead and drill? There is another agriculturalist in a nearby state who claims to have supernatural powers to indicate underground water sources. However, he charges a fee and also travel cost. What is the most Mrs Moore should pay for the services? Before Mrs Moore drills, she could also consult a geologist who can assess the promise of the piece of land. He can tell her whether the prospects are “good” or “poor.” But he is not a perfect predictor. If there is water, the conditional probability is 0,95 that he will say that prospects are good. If there is no water, the conditional probability is 0,85 that he will say poor. What is the value of the information that the geologist could provide? If he charges $70 000, what should Mrs Moore do? What is the value of control for the problem? Are there any real options associated with this problem? What are they and how much are they worth?

Mrs Moore is a agriculturalist and would like to drill for water on her farm. She needs water for irrigation and estimates the benefits of having a successful borehole as $2.0m. However, there is only a 10% chance that she will strike water if she drills and the cost of drilling is $100 000. The alternative is not to drill at all, in which case the benefit will be zero.

Draw a decision tree to represent the problem. Should Mrs Moore go ahead and drill?

There is another agriculturalist in a nearby state who claims to have supernatural

powers to indicate underground water sources. However, he charges a

fee and also travel cost. What is the most Mrs Moore should pay for the services?

Before Mrs Moore drills, she could also consult a geologist who can assess the promise of the piece of land. He can tell her whether the prospects are “good” or “poor.” But he is not a perfect predictor. If there is water, the conditional probability is 0,95 that he will say that prospects are good. If there is no water, the conditional probability is 0,85 that he will say poor. What is

the value of the information that the geologist could provide? If he charges $70 000, what should Mrs Moore do?

What is the value of control for the problem?

Are there any real options associated with this problem? What are they and how much are they worth?