1. The demand (MB) for a good is given by P= 20-Q. The private marginal cost is given by PMC= 6+Q, and the marginal damage function is given by MD = 2+Q.
Note: the optimal tax is the difference in price between the private marginal cost and the social marginal cost at the socially optimal quantity, NOT at the private optimal quantity.
a. Find the social marginal cost curve.
b. Calculate the private optimal Q and social optimal Q
c. Calculate the damage caused by pollution at the private optimal Q and social optimal Q.
d. Find the optimal tax rate that can induce producers to reduce output to social optimal level.
e. Calculate the gain (damage avoided), loss (loss of social surplus caused by less output) and net gain (avoided DWL caused by pollution) of the tax.
2. There is no rule against smoking in the office. Anderson is a smoker, and very selfish. Betty hates smoking. Anderson's supply of pollution abatement: P=4+2x, and Betty's demand for pollution abatement: P=12-2x, where x is the number of cigarettes reduced.
a. What is the optimal pollution abatement level?
b. How should tax be set to achieve the optimal abatement level?
c. Now suppose Anderson would smoke 6 cigarettes a day if there is no rule against smoking. If a cap-and-trade system is used to reduce pollution, then at what level should the cap of pollution be set to?