# Calculate your certainty equivalent for taking this risk, and the associated risk premium.

The residents of Deer Lick, Nebraska are considering allowing the proposed StoneKey Oil Pipeline to have right-of-way to build the pipeline within a couple miles of their town. Without the pipeline, the per capita income in Deer Lick is $36,000 per year. Allowing the pipeline to be built so close to their town would pay additional royalties to the townspeople of $4,000 per capita per year. However, there is a risk – experts have determined that there is a 10% chance the pipeline could leak oil into the town’s groundwater supply, which would cost residents an estimated $20,000 per capita per year in contamination and other environmental costs. [The tiny town’s lawyers have determined that they would not stand a chance against the pipeline’s high-powered attorneys, so if there was an oil leak there would be no chance that the town would win a lawsuit for compensation. That is, compensation for damages would be zero. They would only continue to receive the $4,000 royalty.] Assume you are a resident of Deer Lick:

a. If your utility of wealth were given by the function = ln (), calculate your expected utility from allowing the pipeline to be built. Based on your expected utility, how would you vote? Explain.

b. Calculate your certainty equivalent for taking this risk, and the associated risk premium. Intuitively describe what each of these measures.

c. How high would the probability that the oil would leak into the groundwater supply have to be for you to vote against the pipeline? Why? Let’s say that the townspeople voted to approve the pipeline. To make things simpler for parts (d) and (e), now just use for the utility function, denote per capita income plus royalties as and damages in the event of a leak as (in other words, don’t bother plugging the actual numbers into the explicit form utility function anymore).

d. Suppose the town could collectively invest some amount (dollars per capita per year) to install protective underground barriers that would reduce the probability that any leaked oil would contaminate the groundwater supply – a form of self-protection. If the town has invested per capita per year in self-protection, the probability that a leak will contaminate the groundwater supply is given by the function , where ! < 0. Derive the condition for the optimal amount of investment per capita per year in self-protection? Be sure to provide an intuitive interpretation of the condition you derive.

e. Now suppose that in addition to the public investment in self-protection, the town could privately invest the amount (dollars per person per year) in some form of self-insurance that would reduce damages per capita in the event of a leak. If a leak occurs, and the town invests per person per year in self-insurance, the damages would be given by the function , where ! < 0. Derive the conditions for the jointly optimal investments in self-protection and self-insurance? Be sure to provide intuitive interpretations of the conditions you derive. Part 3 – You will be required to answer one of the following questions (chosen at random by me):