Suppose that two firms emit a certain pollutant. The marginal cost of reducing pollution for each firm is as follows: MC1 = 300e1 and MC2 = 100e2, where e1 and e2 are the amounts (in tons) of emissions reduced by the first and second firms, respectively. Assume that in the absence of government intervention, Firm 1 generates 100 units of emissions and Firm 2 generates 80 units of emissions.

a. Suppose regulators decide to reduce total pollution by 40 units. In order to be cost-effective, how much should each firm cut its pollution?

b. What emissions fee should be imposed to achieve the cost-effective outcome? How much would each firm pay in taxes?

c. Suppose that instead of an emissions fee, the regulatory agency introduces a tradable permit system and issues 140 permits, each of which allows the emission of one ton of pollution. Firm 1 uses its political influence to convince the regulatory agency to issue 100 permits to itself and only 40 permits to Firm 2. How many, if any, permits are traded between the firms? What is the minimum amount of money that must be paid (total) for these permits? By how many tons does each firm end up reducing its pollution?