Assume a firms marginal cost of abatement is given by 3a+1 when a units of pollution are abated. Assume the current daily pollution emission of the firm is given by two units. A new abatement technology becomes available that leads to a reduced marginal cost of abatement given by 1.5a+.5. A) Assume that, in addition to the firm above, there are n other firms (all identical) that also produce two units of pollution. All n firms have already adopted the new technology whereas the firm above has not. Under cap and trade with a daily cap of 5/3 units of pollution per firm, what levels of abatement should the low-cost abatement firms and the high-cost firm choose? [Hint: the abatement levels depend on n. If that is challenging to you, you can pick the special case n=3 and continue on to part B).]

B) Assume that the purchase of the new abatement technology causes a one-time expense of $.5. Assume that the firm minimizes total cost over two periods (today and tomorrow) where expenses tomorrow are discounted by 5%. Assume now that n=3. Will the firm purchase the new abatement technology? (Assume that the firms that sell pollution permits charge exactly the cost that they face for the additional abatement and that the n low cost abaters share the pollution permits sold to the high- cost firm equally.)

C) Argue why a Pigouvian tax is better suited to incentivize firms to adopt lower cost abatement technologies. [Comment: a nice theoretical argument would involve a discussion as to what happens in part A) as n grows large.]