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.**

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tons. The government wants to reduce total SO2 emissions
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firm receiving 140 allowances for free (firms don’t pay for
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