Question

Firm A: initial pollution level = 120, cost to reduce pollution 1 unit = $75

Firm B: initial pollution level = 150, cost to reduce pollution 1 unit = $100

a. Assume that the government decides to cut pollution by 1/3, telling firms that “Starting next year, you will only be permitted to emit 2/3 as much pollution as you currently do.” What is the cost for each firm under this policy?

b. Suppose instead that the government issued permits to each company, entitling them to emit up to 2/3 of their current pollution output. Firms may buy and sell these permits. What is the possible range of prices for which both firms would be willing to buy/sell?

c. Assume that the firms agree to a price in the range you found in part b. What firm buys permits and which sells? How many permits are exchanged?

d. What is the total cost of pollution reduction now? Hint: your answer should make sense when you compare it to part a

Answer 1

a)

Abatement required for firm A=120*(1/3)=40 units

Cost of abatement for firm A=TACa=40*75=$3000

Abatement required for firm B=150*(1/3)=50 units

Cost of abatement for firm B=TACb=50*100=$5000

b)

Cost of permit will be somewhere between their marginal abatement costs.

So, Cost of permit will lie in the range given by ($75,$100)

c)

Marginal abatement cost is higher for firm B. It will buy permits.

Marginal abatement cost is lower for firm A. It will sell permits.

Total abatement required=40+50=90 units

Pollution created by firm A is higher than the total abatement required. So, it can afford to abate all of the pollution. It can sell all of its permits. but permits required by firm B is only 50,

Number of permits exchanged=50

d)

Total abatement cost in absence of permints=TACa+TACb=3000+5000=$8000

After the permits are traded,

Abatement required for firm A=40+50=90 units

Cost of abatement for firm A=TACa=90*75=$6750

Abatement required for firm B=50-50=0 units

Cost of abatement for firm B=TACb=0*100=$0

Total Cost of abatement after permits are traded=6750+0=$6750

We can see that the total abatement cost is reduced if permits can be traded.