Wildcat Co. has to decide whether or not to drill an oil well. It has $100 current income. Drilling would cost $100; if oil were struck, the company would receive $200 for the oil. If the field is dry, nothing is recovered.

(a) Suppose Wildcat's U-function is U=y where y is income. Suppose the probability of striking oil is 0.6. Should Wildcat drill? At what probability would Wildcat be just indifferent between drilling or not?

(b) Now suppose the U-function is U=2y1/2. Is Wildcat risk averse? Using this function, answer question (a).

(c) Suppose for $20, Wildcat could run a test that would determine for certain whether the field is wet or dry. The probability of a positive test is .6. Would the Wildcat with utility as in (a) do this test? (Assume that if the field is wet, they can borrow at zero interest the extra $20 needed to drill - to be repaid immediately.) What is the maximum amount Wildcat would pay for the test?  For which U-function does the company value the test higher?