Problem 1.

A local energy provider offers a landowner $180,000 for the exploration rights to natural gas on a certain site and the option for future development. This option, if exercised, is worth an additional $1,800,000 to the landowner, but this will occur only if natural gas is discovered during the exploration phase. The landowner, believing that the energy company's interest in the site is a good indication that gas is present, is tempted to develop the field herself. To do so, she must contract with local experts in natural gas exploration and development. The initial cost for such a contract is $300,000, which is lost forever if no gas is found on the site. If gas is discovered, however, the landowner expects to earn a net profit of $6,000,000. The landowner estimates the probability of finding gas on this site to be 60%.

Suppose that, instead of making a decision right now between developing the site herself or contracting with the local energy provider, she can, at a cost of $90,000, request that a soundings test be performed on the site where natural gas is believed to be present. The company that conducts the soundings concedes that 30% of the time the test will indicate that no gas is present when it actually is. When natural gas is not present in a particular site, the soundings test is accurate 90% of the time.

A.Assume that the landowner pays for the soundings test and the test indicates that gas is present. What is the revised estimate of the probability of finding gas on this site?

B.Given that the landowner pays for the soundings test and the test indicates that gas is not present, what is the landowner's revised estimate of the probability of not finding gas on this site?

C.What is the optimal action of the landowner? Should she request the soundings test at a cost of $90,000? If she doesn't request the test, should she contract with the local energy provider or should she develop the site herself? If she does request the soundings test, what should she do if the test indicates if gas is present? If the test indicates that gas is not present?

D.What is the most (if anything) that the landowner would be willing to spend on the soundings test?