Assignment:
1. In western Wyoming, natural gas production produces a significant amount of ozone emissions. On really cold days in the winter, temperature inversions trap the ozone near the ground, and the unusually high levels of ozone in the atmosphere cause significant health issues for residents
a. Using a simple supply and demand diagram, model this negative externality associated with natural gas production. Be sure to show both the competitive and socially optimal equilibrium prices and output of natural gas.
b. Using your diagram, show the increase in economic welfare that would result from moving from the competitive to the socially optimal equilibrium
c. How might the Wyoming state government construct a policy that would induce the natural gas companies to produce the socially optimal amount of natural gas? Mathematically demonstrate your answer.
2. Give an example of an environmental good for which the contingent valuation method could be used to estimate its value.
a. Explain in detail how the contingent valuation method would be used to estimate the value of the environmental good.
b. What sorts of issues can arise? How might they be addressed? Note: You might refer to Hanemann (1994) to help answer this part.
c. Briefly describe another valuation method that could be used to value the same environmental good, and explain how the alternative method you chose differs from the contingent valuation method.
3. What is a public good?
a. Give an example of a public good.
b. What is the key market failure associated with public good provision?
What is the result of this market failure in terms of how much of the public good is provided?
Note: A diagram would go a long way in helping show that you understand the answer to this question, but it must be accompanied by a complete and intuitive description of what you have drawn.
c. How might a government entity estimate the value of the public good you chose?
d. How might they implement a policy to provide the socially optimal amount of your public good?
4. 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.
5. Using a model similar to that found in Hartwick& Oleweiler, derive the condition for the efficient extraction of a depletable resource, and solve for the optimal amount extracted in any two consecutive periods, !and !!! . Be sure to interpret the condition you derive. Assume the following:
a. The initial stock of the resource is ! .
b. The discount rate is .
c. The final period is .
d. The firm is a monopoly, and the inverse market demand curve for the extracted resource is ! = - ! . !
e. The extraction cost curve is ! = ! ! . ! 6. Consider a forest economy in which all timber stands are of equal quality and privately owned. Assume that the net price of harvested timber, , is constant over time, as is the cost of planting a new stand of trees,. Derive and intuitively explain Faustmann's rule for the optimal timber rotation for a representative stand of trees, denoted by . How and why does the optimal rotation change if
a) the discount rate increases,
b) the cost of planting increases, and
c) the net price of timber increases?