Suppose that the (external) damage done by pollution is known to be MD = 300 + 5Q, and the (private) cost and benefit are given by MC = 100 + 2Q and MB = D0 − 2Q, where D0 is not precisely known.
a. If D0 = 1,000, what would be the optimal quantity? What tax would be necessary in order for that to be the equilibrium quantity?
b. Suppose that, based on the result from part a, a cap-and-trade system is imposed to allow the optimal quantity of pollution to be produced. If D0 = 900, what would be the deadweight loss associated with having the wrong quantity?
c. Supposed that, based on the result from part a, a tax is imposed to allow the optimal quantity of pollution to be produced. If D0 = 900, what would be the deadweight loss associated with having the wrong tax level?
d. If D0 is not exactly known, which is likely to give better results, a cap-and-trade system or a tax? What would be the answer to this question if the marginal damage were 300 + 3Q instead of 300 + 5Q?