Three sources with constant MC curves

Suppose a particular pollutant is produced by three sources. Initially, none of the sources is abating emissions and each is emitting 30 tons of pollution. The marginal abatement costs of the sources are as follows: MC1 = $100, MC2 = $200, MC3 = $300. (That is, the marginal cost of abating pollution from source 1 is $100 for each unit eliminated, etc.) The marginal benefit of abatement is given by MB = $1000 - 16 Qa, where Qa is the total quantity of abatement.

1. Find the efficient amount of abatement for each firm. Be sure to show all your work and explain your reasoning. Also, calculate the cost to each firm of cleaning up its emissions. Do you think the firms would regard this as fair? Discuss.

2. Now consider solving the problem by using a tradable permit policy. What quantity of permits should be issued? What will the market price of a permit be? How would you distribute them if you wanted to equalize the overall cost of abatement across all three firms? (Please calculate the specific quantity of permits to be given to each firm.) Would the firms prefer this or an emissions tax policy? Explain.