Per the Kyoto Protocol, European countries have targeted a reduction of CO2 emissions. There are two main types of coal-fire plants in the EU: one type is designed to be able to be retrofitted with abatement equipment at a lower cost than the other type. The EU government has given its economists the job of figuring out the least costly way to reach the goal of reducing pollution by 120 tons of CO2 this year. The marginal abatement costs for each type of plant are as follows: Type 1: MC1 = 5q1 Type 2: MC2 = 3q2 where q1 is the total tons of CO2 removed by type 1 plants where q2 is the total tons of CO2 removed by type 2 plant Instead,

The EU implements an emissions tax.

a. Find the tax per ton of carbon that would allow the EU's target to be reached at the lowest cost.

b. Draw the graph and label the tax. Using one of the firms as an example, explain the process by which economic incentives move the firms to the efficient q of abatement.

c. Using your calculations from #1 and additional calculations here, show that the using the tax is the efficient method of abating pollution.