Problem: In July 1997, the EPA announced new air quality standards for small particulate matter (2.5 micrometers in diameter) referred to as PM2.5.  Previously particulate matter less than 10 microns in diameter were regulated.  Steel mills are a major source of these smaller particles and therefore must find ways to abate.  Consider the following hypothetical model of two steel plants, one owned by Bethlehem Steel (B) and one owned by National Steel (N), both located in Pittsburgh, Pennsylvania:

Bethlehem: MC_B = 1.2A_B

TC_B .6(A_B)²

National: MC_N = 0.3A_N

TC_N = 0.15(A_N)²

Assume that each plant emits 40 units of PM2.5 for a total of 80 units.  In order for the Pittsburgh area to meet the new standard, the EPA determines that the combined abatement for both plants must total 30 units.

Question 1: Assuming the new abatement standard is implemented uniformly between the two firms, find the total cost of abatement for each firm and the overall total cost of abatement.  Show your work. 

Question 2: Mathematically or graphically demonstrate that your answer to (a) is NOT cost effective.

Question 3: Find the cost effective solution for 30 total units of abatement.  Show your work and clearly indicate both A_Band A_N. Note that this is similar to the "Puzzle" on page 317 but with MC as a function of abatement levels (level of pollution reduced) rather than as a function of pollution.  But see the solution to that puzzle if you need help solving this problem. 

Question 4: Verify that your solution in (c) is cost effective by showing that the marginal cost of abatement is the same for both firms.

Question 5: Under the cost effective solution, which firm experiences increased total costs relative to the uniform abatement policy?  Why?  What happens to the total costs for the other firm?  Why?

Question 6: Calculate the total cost savings associated with the cost effective solution relative to the uniform abatement standard.  Show your work.