Suppose there are two rms, each of which can emit, at most, 25 tons of pollution into the environment per year. Assume that each firm maximizes their profit at this pollution level, implying that they will each emit 25 tons unless subject to a regulation or penalty. However, each firm also has the capacity to abate some or all of their pollution, meaning that they can choose an abatement level anywhere between 0 and 25 tons (0 tons of abatement implies 25 tons of pollution and 25 tons of abatement implies 0 tons of pollution). Let A₁ denote Firm 1's abatement and let A₂ denote Firm 2's abatement. The firms' marginal abatement cost (MAC) functions are shown below, where MAC is denominated in dollars per ton, and A₁ and A₂ are denominated in tons. (Assume that there are no fixed costs associated with pollution abatement.)

Firm 1: MAC₁ = 1.5A₁

Firm 2: MAC₂ = 2.0A₂

a) Suppose that a pollution tax of $21 per ton were enacted. Explain in words and with a clearly labeled graph why 10 tons of abatement is not Firm 1's optimal response to this $21 per ton tax.

b) What are Firm 1's total abatement costs and total tax burden when it abates 10 tons? Identify these amounts on the graph you drew for a) and explain how Firm 1 could lower its combination of tax costs and abatement costs by choosing a different abatement level. Would Firm 1 like to increase or decrease abatement (relative to 10 tons) and why?

c) Suppose the EPA decided that 30 tons of pollution abatement was socially desirable and they mandated that each firm reduce 15 tons. Evaluate the cost implications of this policy. Would it be possible to improve on this initial abatement allocation? If so, what would be the gains?

d) If Firm 1 were the only source of pollution and the marginal social benefits (MSB) of pollution abatement were given by MSB = 40 - 1.8A₁, at what level would you recommend that the regulator set a pollution tax? Why?