Two large factories are operating in the same area, causing serious SO₂ - emissions ( 70 and 40 units) . The authorities would like to reduce the emissions of ₂ to 60 units using a tax. The total abatement cost curves of the factories are: T₁ = 2¹₂T₂ = 3²₂ (where " " means the amount of removed pollution) .
How many units of pollution will each company remove and what is the tax rate necessary to achieve this?