2. Externalities: Abatement Costs (8 points) Suppose that there are two firms that produce lightbulbs: GreenBulb and SludgeTech. Currently, both types of firms behave the same, and both have no private marginal benefit from reducing pollution, but they have different marginal costs of reducing pollution, given by the following:

GreenBulb : MCG = 10 + 2AG

SludgeT ech : MCS = 20 + 4AS

where Ai is the quantity of pollution abated (that is removed or offset) by the firm i G, S, measured in tons of carbon dioxide. Suppose that, without government intervention, each firm would emit 30 tons of carbon dioxide.

(a) If the government issued a policy that fined firms $40 for every unit of pollution produced, how many tons of carbon dioxide are abated in total across firms? (Assume that it is profitable for the firms to operate regardless of the size of the fine or the abatement costs that they incur.) (2 points)

(b) Suppose that these marginal cost curves correspond to total abatement cost curves:

GreenBulb : CG = 10AG + A 2 G

SludgeT ech : CS = 20AS + 2A 2 S

What is the total cost of abatement induced by the fine? (1 point)

(c) Prove that $40 is the optimal fine if you would like to achieve 20 tons of abatement [Hint: How much would your order each firm to abate if you were trying to minimize total cost?](4 points)