Problem
Suppose the total benefits of pollution abatement in the cement industry are equal to 240Q-Q2 where Q is the quantity of abatement. Suppose the marginal costs of abatement are uncertain: there is a 50% chance the marginal abatement costs is equal to 40, and there is a 50% chance the marginal abatement costs are equal to 80.
I. How much abatement occurs in the absence of any government intervention?
II. If the government knew for certain that the marginal abatement costs were 80, what would be the efficient level of abatement? And if the government knew the marginal abatement costs were 40, how much abatement would be efficient? Identify policy instruments the government could use to achieve the efficient level of abatement if the marginal abatement costs were known.
III. What is the expected marginal cost of abatement? Amid the uncertainty, what is the welfare maximizing, i.e., efficient price and quantity of abatement?
IV. What is the magnitude of the expected deadweight loss (DWL) if the government implements the efficient quantity instrument? (Hint: begin by identifying the DWL in each state of the world, i.e., when marginal abatement cost is 40 and where it is 80 and multiply by the probability each outcome occurs).
V. What is the deadweight loss from implementing a price instrument amid the uncertainty if the high marginal abatement costs are realized? Is the DWL from the price instrument bigger or smaller than this if the low marginal abatement costs are realized? So is the expected deadweight loss from the price instrument bigger and smaller than the expected deadweight loss from the quantity instrument?