Part A, Value of Information

Suppose a city is considering developing a brownfield site but believes there is a 50% chance the site is contaminated with hazardous waste. If the site is clean (call that state "C"), the net present value of development will be $10 million. However, if the site is discovered to be contaminated during the construction process (call that state "D" for "dirty"), the site will have to be remediated and the net present value will be -$20 million.

It is possible to test the site for contamination prior to making the decision to develop. However, the test costs $1 million and is imperfect: when contamination is present, the test will fail to detect it 20% of the time. Moreover, the test has a 10% chance of falsely indicating that a clean site is contaminated. What is the expected present value of the test? Should the city buy it? In doing your calculations, you should assume that if the city chooses not to develop, it does not have to pay any remediation costs -- it only has to pay for the test itself.

Please note that since all costs and payoffs are already expressed in present value terms, you do not need to do any present value calculations in this problem.

Part B, Risk Aversion

An individual saving for retirement has a choice of three investments. Option A would have a 20% chance of producing $1 million and an 80% chance of producing $10,000.  Option B would have a 30% chance of producing $250,000 and a 70% chance of producing $60,000.  Option C would produce $100,000 for certain. The person is risk averse and will choose the option that maximizes his expected utility. The person's ordinary (ex post) utility from a payoff of x dollars is u(x) = x^0.5 (that is, the square root of x).

Please evaluate each of the options: calculate its expected value, its expected utility, and its certainty equivalent.  Which option would the individual choose? Would a risk neutral agent choose a different alternative?