Question

Two polluting firms emit 200 tons of SO2 each, with Marginal Abatement Costs given by MAC1= 2X1 and MAC2= 3X2, respectively. Xi represents the level of abatement for each firm i, in tons.

The government wants to reduce total SO2 emissions by 30% and decides to impose a uniform cap on emissions, with each firm receiving 140 allowances for free (firms don’t pay for allowance).

a) In a first moment assume polluters are not allowed to trade, so each firm abates 60 units. What is the Marginal Abatement Cost (MAC) and the Total Abatement Cost (TAC) for each firm?

b) The government now allows polluters to trade permits, as in cap-and-trade. What is the abatement level of each firm? In other words, find X1 and X2 under this policy.

c) What are the “new” Total Abatement Costs (TAC1 and TAC2) after the trade is allowed? Compare your answer with the situation before the trade was allowed (part a). Did the overall Total Abatement Cost (TAC1 + TAC2) increase or decrease?

Answer 1

a)

Each firm is required to abate 60 units.

MAC for firm 1=2X1=2*60=$120

MAC for firm 2=3X1=3*60=$180

Total abatement cost for firm 1 is given as

Total abatement cost for firm 2 is given as

b)

In case X1+X2=120

or X2=120-X1

Set MAC1=MAC2 for cost minimization

2X1=3X2

2X1=3*(120-X1)

2X1=360-3X1

5X1=360

X1=360/5=72 (abatement level for firm 1)

X2=120-X1=120-72 =48 (abatement level for firm 2)

c)

Total abatement cost for firm 1 is given as

Total abatement cost for firm 2 is given as

TAC after trade able permits=5184+3456=$8640

TAC before trade able permits=3600+5400=$9000

TAC has decreased after trade able permits are issued.