Reducing the emission level and tradable permits.
Two firms X and Y each dumped 30 tons of sulphur dioxide into the air last year. The EPA wants to reduce total emissions of SO2 by 12 tons this year. The following table gives the cost to each firm of reducing its SO2 output by the amount specified. For instance, if X reduced its SO2 output by 1 ton its cost would increase by 10, and if instead X reduced its SO2 output by 2 tons its cost would increase by 15 (not 10 + 15). (To simplify the calculations, assume that when SO2 output.) Each pollution permit entitles the holder to dump one ton of SO2. Pollution rights can be traded, and the following problems ask for some critical values at equilibrium, under two different scenarios.

1 
2 
3 
4 
5 
6 
7 
8 
9 
10 
11 
12 
X 
10 
15 
20 
25 
40 
50 
55 
60 
65 
70 
75 
80 
Y 
4 
6 
8 
12 
16 
20 
25 
30 
38 
45 
55 
70 
For each of the following two scenarios answer problems A and B.
A. By how much will each firm reduce its SO2 output? Which firm will buy permits, which firm will sell them, and how many permits will be exchanged?
B. The total amount of money that is exchanged among the two company must be more than what number and less than what number?