In: Economics
Suppose that you have been hired by the Environmental Protection Agency (EPA) and your first project is answer the questions below based on the following information:
MD = 3E,
MACL = 10 – 2E,
MACH = 60 – 2E,
where MD is the marginal damage, MACL is the marginal abatement cost under the “low” scenario, MACHis the marginal abatement cost under the “high” scenario, and E represents pollution level. The agency is uncertain about the true marginal cost and believes that the probability of MCL is 40% and the probability of MCH is 60%.
a) Derive the expected marginal abatement cost (E(MAC)) equation. Hint: Since there are two possible marginal abatement cost outcomes, you need to multiply each marginal cost equation by the corresponding probability and sum them together. This will give you the expected marginal cost equation.
b) What is the allocative efficient pollution level? Hint: Remember that at the allocative efficient outcome, MAC equals MD. In this case you have to set the expected MAC equation that you derived in part a) equal to the MD equation to get the allocative efficient pollution level.
c) Draw a graph showing the allocative efficient level of pollution. Label this point “A”. Make sure to label all the curves. (MAC and MD on the vertical axis. E on the horizontal axis). Make sure to include the value of the horizontal and vertical intercepts for the expected MAC curve. Hint: In this case you have to draw two curves: the MD curve and the expected MAC curve.
d) What is the fee (tax) per unit of emission required to achieve the allocative efficient level of pollution reduction? Explain. Hint: Remember that the emission fee should be set equal to the amount of marginal damage that occurs at to the allocative efficient level of pollution.
e) Assume that the EPA introduces the fee (tax) per unit of emission you found in part d). If the actual marginal abatement cost happens to be MACL, what would be the emission level and the marginal damage under this fee (tax) system? Hint: Remember that under an emission tax system, a firm will choose to emit as long as the fee (tax) per emission is lower than the marginal abatement cost and vice versa.