Two firms, X and Y, have access to 5 production processes (all of which produce the same quantity of retail
output). Each production process has a different cost and gives off a different amount of pollution. The daily
costs of the processes and the corresponding number of tons of smoke emitted are as shown in the following
table:
Process A B C D E
Smoke 4 tons/day 3 tons/day 2 tons/day 1 ton/day 0 tons/day
Cost of X 60 70 100 200 400
Cost of Y 80 180 300 430 600

(a) If pollution is unregulated, what will be the daily smoke emission?

(b) The city council wants to curb smoke emissions by 50 percent. To accomplish this, it requires
each firm to curb its emissions by 50 percent. What will be the total cost to society of this policy?

(c) The city council wants to curb smoke emissions by 50 percent. Now, it sets a tax of T dollars per
day on each ton of smoke emitted. How large will T have to be to effect the desired reduction?

(d) Instead of taxing pollution, the city council decides to auction off four permits, each of which
entitles the bearer to emit 1 ton of smoke per day. No smoke may be emitted without a permit.
Suppose the government conducts the auction by starting at $1 and asking how many permits
each firm wants to buy at that price. If the total is more than four, it then raises the price by $1
and asks again, and so on, until the total quantity of demanded permits falls to four. How much
will each permit sell for in this auction? How many permits will each firm buy?