Assume that two power plants, Firm 1 and Firm 2, release sulfur dioxide (SO₂)in a small urban community that exceeds the emissions standard. To meet the standard, 30 units of SO₂ must be abated in total. The two firms face the following abatement costs:

MAC₁ = 16 + 0.5A₁

MAC₂ = 10 + 2.5A₂,

where costs are measured in thousands of dollars.

a. Prove that a uniform standard will not meet the cost-effectiveness criterion.

b. Determine how the abatement levels should be reallocated across the two firms to minimize costs.