Question

The senior executives of an oil company are trying to decide whether to drill for oil in a particular field in the Gulf of Mexico. It costs the company $300,000 to drill in the selected field. Company executives believe that if oil is found in this field its estimated value will be $1,800,000. At present, this oil company believes that there is a 48% chance that the selected field actually contains oil. Before drilling, the company can hire a geologist at a cost of $30,000 to prepare a report that contains a recommendation regarding drilling in the selected field. There is a 55% chance that the geologist will issue a favorable recommendation and a 45% chance that the geologist will issue an unfavorable recommendation. Given a favorable recommendation from the geologist, there is a 75% chance that the field actually contains oil. Given an unfavorable recommendation from geologist, there is a 15% chance that the field actually contains oil.

1. Assuming that this oil company wishes to maximize its expected net earnings, determine its optimal strategy through the use of a decision tree.

Answer 1

The company can choose to hire a geologist or not hire a geologist.

If the company does not hire a geologist and goes about drilling, there is a 52% chance it will not get oil and lose the $300,000 or there is 48% chance it will gain net $1,500,000 (1,800,000 - $300,000)

So the overall expected earnings here for the company will be 52% X (-300000) + 48% X 1500000 = $564,000

Now let us consider the decision tree where the company decides to hire a geologist the decision tree for which is given below:

As can be seen, of the geologist gives favorable recommendation which has a 55% change, the chance of getting oil is 75% with net payoff of 1500000 and net loss of -300000 with probability of 25%

So total payoff in this case os 1,050,000 (75%X1500000 - 25%x300000)

For unfavorable recommendation, the payoff is 1500000 with 15% chance and -300000 with 85% change; so net payoff is -30,000 (15%X1500000 - 85%X300000)

Therefore to hire a geologist, the net payoff is 55%X10,40,000 - 45% X 30000 = 564,000

Actually since we are paying $30,000 to hire the geologist, the net payoff will be $534,000 in this case

In the original case without hiring the geologiest the company was getting a better net payoff.

Hence from the pure strategy and net payoff point of view the company may choose not to hire a geologist.