1. Suppose that two firms emit a certain pollutant. The marginal cost of reducing pollution for each firm is as follows: MC₁=350e₁ and MC₂=150e_2, where e₁ and e₂ are the amounts (in tons) of emission reduced by the first and second firm respectively. Assume that in the absence of government intervention Firm 1 generates 100 units of emissions and Firm 2 generates 80 units of emissions.

1. Suppose regulators decide to reduce the total pollution by 50 units. In order to be cost efficient, how much should each firm cut its emission?

2. What emission fee should be imposed to achieve the cost-efficient outcome? How much each firm pay in taxes?

3. Suppose that instead of an emission fee, the regulatory agency introduces a tradable permit system and issues 130 permits each of which allows an emission of one unit of pollution and distributes these equally among the firms (i.e., 65 each). How many permits are traded among two firms (i.e, which firms sells and how many). What is the minimum amount of money must be paid (in total) for these permits? By how many units each firm ends up reducing its pollution.