What is the allocative efficient pollution level draw a

Question

Problem

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:

(1) MD = 3E,

(2) MAC_L = 10 - 2E,

(3) MAC_H = 60 - 2E,

where MD is the marginal damage, MAC_L is the marginal abatement cost under the "low" scenario, MAC_H is 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 MC_L is 40% and the probability of MC_H is 60%.

a) Derive the expected marginal abatement cost (E(MAC)) equation.

b) What is 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.

d) What is the fee (tax) per unit of emission required to achieve the allocative efficient level of pollution reduction? Explain.

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 MAC_L, what would be the emission level and the marginal damage under this fee (tax) system?