The residents of Deer Lick, Nebraska are considering allowing the proposed StoneKey Oil Pipeline to have the right-of-way to build the pipeline within a couple of 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 towns groundwater supply, which would cost residents an estimated $20,000 per capita per year in contamination and other environmental costs. [The tiny towns lawyers have determined that they would not stand a chance against the pipelines 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 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?

d. Lets say that the townspeople voted to approve the pipeline. Now suppose the town could collectively invest the 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 a leak occurs, and 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 (). 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 derived.

e. Now (going back to the original probability of a 10% chance of a leak, which we will leave as being exogenously determined), suppose the townspeople voted down the public investment in self-protection, but you could privately invest the amount (dollars per year) in some form of self-insurance that would reduce your damages in the event of a leak. If a leak occurs, and you invest per year in self-insurance, the damages (per year) to you would be given by the function (). Derive the condition for your privately optimal investment in self-insurance? Be sure to provide an intuitive interpretation of the condition you derived.

f. Now assume that both self-protection and self-insurance measures could be taken simultaneously. What conditions define the optimal level of each when both can be employed jointly? Be sure to provide an intuitive interpretation of the conditions you derived.

g. Now assume that a given residents exposure to a harmful oil leak, , was continuously distributed over the range [,] and that the damages suffered by an individual are a function of his/her exposure. i) Recast the expected utility function for continuously distributed exposure, carefully explaining each part of the expected utility function. ii) Intuitively explain how investments in self-protection and self-insurance affect the distributions of both radiation exposure and damages.