Question

Two firms, Sludge Oil and Northwest Lumber, have access to five production processes, each one of which 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 (smoke)	A (4 tons/day)	B (3 tons/day)	C (2 tons/day)	D (1 ton/day)	E (0 tons/day)
Cost to Sludge Oil ($/day)	50	70	120	200	500
Cost to Northwest Lumber ($/day)	100	180	500	1,000	2,000

a. If pollution is unregulated, and the firms have no incentive to reduce pollution, which process will each firm use, and what will be the total daily smoke emission?

    The firms will use process    (Click to select)   A   B   C   D   E  .

    The smoke emission would be _______ tons per day.

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 increase in total cost to society due to this policy?

    Total cost to society will be $ _____ .

c. The City Council again wants to curb emissions by half, so it sets a tax of $T per day on each ton of smoke emitted. How large will Thave to be to effect the desired reduction?

    T would have to be $______ .

    

    What is the total cost to society of this policy?

    Total cost would be $ ______

Answer 1

1. both firms will go with least cost option ie. 4 tons/ day. Process A followed by both. Total Smoke emissions = 8 tons/day

2. Total Cost to society increased by: 500 + 120 - 50 - 100 = 470

3. Tax rate = T

Smoke Quantity above the desired limit* T = 470

=> (2*4+2*3)*T > (50+70+100+180)

=> 14*T > 400 => T> 400/14 = $ 28.57

4. Total Cost to Society = 400