An economy has two firms and 75 consumers. The two firms pollute. Firm 1 has a savings function S1(e)=20e−2.5e2, where e is the quantity of emissions from the firm. Firm 2 has a savings function S2(e)=10e−5e2. Each of the consumers faces damages D(e)=0.05e2, where e is the total amount of emissions that the consumer is exposed to.

1. 1. What are the firm-level and aggregate marginal savings functions? Include a graph.
2. 2. How much pollution does each firm emit if there is no environmental regulation?
3. 3. What is the aggregate marginal damage function? Add the marginal damage function to your graph from part A.
4. 4. What is the optimal level of aggregate emissions and optimal level of emissions from each firm? Label these on your graph.
5. 5. What is the appropriate Pigouvian fee? At that level of tax, how much does each firm abate?
6. 6. The government decides to use a cap-and-trade system to reduce emissions to optimal levels. For how many units of emissions does it allocate permits?
7. 7. If the government gives each firm an equal number of emissions permits, do firms trade? If so, how many units (or fraction thereof) does each firm buy or sell, and at what price?
8. 8. Suppose the government does not know the firm's marginal savings function for certain. There is a 50% chance the aggregate MS curve should be shifted 1 unit higher and 50% chance it should be shifted 1 unit lower. Given this uncertainty, which policy is preferable, emissions fees or tradable permits? Explain why.