Question

1. Consider the problem of two polluting sources in the region, each of which generated 10 units of pollution for a total of 20 units released into the environment. The government determined that emissions must be reduced by 12 units across the region to achieve the ”socially desirable level of pollu- tion”. Each firm faces different abatement cost conditions modelled as follows: for Polluter 1, marginal abatement cost is MAC1 = 26- 2.6E1. For Polluter 2, marginal abatement cost is MAC2 = 5.2- 0.52E2.

(a) What is the TAC for Polluter 1 and Polluter 2?

Consider now other possible policies like a tradable emission permits (TEP’s) system and an emission tax as ways to achieve the cap of 8 units of emissions.

(b) Assume that the government imposes emission charge set at $4 for each polluter. Show how each firm responses to tax. Does $4 unit tax achieve the 12-unit abatement standard? If not, is $4 unit tax too high or too low? Discuss.

(c) Assume that the government decides to issue permits rather than im- pose tax. It issues 8 permits, each of which allows the bearer to emit 1 unit of pollution. The government allocates 4 permits to each polluter.

1. If the permits system does not allow for trading, what would be each firm’s response - cost, abatement required to this allocation?

2. Assume now that trading is allowed and that two firms agree on the purchase and sale of permit at a price of $8.00. What would be each firm’s response - cost, abatement required, revenue to this price?

3. Does the outcome from part (ii) represent the cost effective solu- tion? If yes - why? If not, describe what happens next.

Answer 1

a) Each firm is required to reduce its emission by 6 units of pollution.

MAC1= 26-2.6E1

TAC1= MAC1*E1

=( 26-2.6E1 )*E1

putting E1=6

TAC1=( 26-15.6 )*6= 62.4

similarly,

MAC2= 5.2-.52E2

TAC2= (5.2-.52E2)*E2

Putting E2=6

TAC2= 12.48

b) $4 tax on each unit of pollution results in each source paying 4*10=$40 for 10 emissions.

$40>TAC1

so paying $40 and emitting 10 units is profitable for source 1 than incurring total abatement cost of $62.4 in order to reduce emissions by 6 units.

But $40< TAC2

So its better for source 2 to not produce 10 emissions and instead abate 6 emissions.

c) each source can now emit only 4 units.

if trading is allowed, then to emit 1 more unit, a source requires 1 permit which costs $8.

marginal abatement cost for source 1 is 26-2.6*1= 26-2.6= $23.4

emitting is better than abatement for source 1

for source 2, abatment cost is 5.2-.52= $4.68

abatement is better than emitting

so source 2 can sell its permits to source1 and both can increase their own welfare in doing so.