A threshold pollutant with three sources

Suppose a particular pollutant is emitted by three sources and is initially uncontrolled. Source 1 emits 400 tons and can abate its emissions at a marginal cost given by MC1=Q1, where Q1 is the amount of abatement. Source 2 emits 800 tons and can abate at a cost given by MC2=2*Q2. Source 3 also emits 800 tons but its marginal cost of abatement is constant at $300. The damages caused by the pollutant depend on how much is being emitted. When the level of pollution is 1500 tons or less, the damage caused by an additional unit of pollution is $100; when emissions are greater than 1500 tons, the marginal damage is much higher: $1000.

1. Determine the efficient level of abatement. How much should each source clean up? What will each source end up spending on abatement? What will the total amount spent onabatement be?
2. Suppose the government decides to use a command and control policy to reduce the problem. It calculates the percentage reduction in overall emissions from part (1) and then requireseach firm to reduce its emissions by that fraction. For example, if you showed in part (1) that overall emissions should be reduced by 20% then the command and control policy wouldrequire that each source eliminate 20% of its emissions. How much will each source end up paying for pollution abatement? Discuss how this compares to the results from part (1). Is it better or worse? Why?
3. Suppose the government wanted to use a tradable permit policy instead. Design a policy that would achieve the efficient amount of abatement while spreading the overall cost betweenthe firms according to their shares in the initial emissions. (For example, firm 2 accounts for 40% of initial emissions so it should pay 40% of the cleanup costs.) How many permitswould you distribute to each firm? What would the price of a permit be in equilibrium?