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?

the price

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?