Town A suffers from pollution by two firms which we will call Firm 1 and Firm 2. The two firms emit 100 units of pollution together, 60 units emitted by Firm 1 and 40 units emitted by Firm 2. Residents of Town A would like the local government to regulate these two firms so that pollution is reduced by 45 units. Marginal pollution control costs for the two firms are given in the table below. Firm Emissions Firm 1 Firm 2 Reduction Marginal Cost ($) Marginal Cost ($) 5 5 10 10 10 20 15 15 30 20 20 40 25 25 50 30 30 60 35 35 70 40 40 80 45 45 50 50 55 55 60 60 If the local government decides to adopt a cap-and-trade policy to achieve the desired level of pollution and plans to auction off the allowances to the highest bidder: a) How many allowances will the control authority auction off? Why? b) Assuming no market power, how many of the allowances would each firm be expected to buy? Why? c) Assuming that demand equals supply, what price would be paid for those allowances? Why? d) If the control authority decided to use an emissions tax rather than cap-and-trade, what tax rate would achieve the 45 unit reduction cost effectively