Question

Two polluting firms emit 200 tons of SO₂ each, with Marginal Abatement Costs given by MAC₁= 2X₁ and MAC₂= 3X₂, respectively. X_i 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).

1. What is the market price of SO₂ abatement?

2. How many permits are traded between firms, who is selling to who, and what are the Total Emission Fees (TEF) for each firm?

3. What is the sum of all emission fees under cap-and-trade, TEF₁ + TEF₂?

4. Instead of cap-and-trade, the government decides to impose a pollution tax equivalent to the market price of SO2 you found on part d. Without any further calculations, indicate what is the abatement level for each firm under the pollution tax.

5. What would be the total emission fees (TEF) under the pollution tax? Compare it with your answer for cap-and-trade. How would this comparison be if the initial cap-and-trade permits (allowances) were sold in an auction, and not given for free?

Answer 1

A) MAC1=2x1 ,x1= MAC1/2

MAC2=3x2. ,x2=MAC2/3

Aggregate MAC: x=5MAC/6

MAC=1.2x

So total abatement=60+60=120

MAC=1.2*120=144

So market price of permit is 144$.

B)x1=144/2=72

X2=144/3=48

So firm 1 abate more than it required ,which tells that firm 1 is selling its permit.

Firm 2 abatement is less than required ,which means that firm 2 is buying the permit.

So trade of permit=12 units.

TEF1=-144*12=-1728( it benefit by selling permit)

TEF2=144*12=1728

C)TEF1+TEF2=-1728+1728=0

D)under this pollution tax =144$, the ABATEMENT levels are,

x1=72

X2=48