Question

There are 3 industrial firms in Happy Valley:

Firm	Initial Pollution Level	Cost of Reducing Pollution by 1 Unit
A	70 units	$30
B	60 units	$10
C	80 units	$50

The government wants to reduce pollution to 150 units and gives each firm 50 pollution permits.

1. What is the total cost of pollution abatement if the permits are not tradable?

2. What is the total cost of pollution abatement if the permits are traded at a

   price of $20 each?

Answer 1

The current pollution emission level is equal to,

= Initial pollution level of firm A + initial pollution level of form B + initial pollution level of firm C

= 70 + 60 + 80

= 210 units of pollution.

Now the government wants to reduce the pollution level to 150 units and in order to do that it has issued a 50 pollution permits to each firm so that each firm can only emit 50 unit of pollution.

So firm A will reduce pollution by,

= initial pollution level - pollution allowed by permit

= 70 - 50

= 20

And cost of reducing pollution for firm A is equal to $30 per unit so the total cost of abatement for firm A will be equal to,

= 30 × 20 = $600.

Similarly the firm B will reduce the pollution by,

= 60 - 50

= 10

And the cost of abatement for firm B is equal to $10 per unit so the total cost of abatement for firm B will be equal to,

= $10 × 10

= $100

Similarly firm C will reduce the pollution by,

= 80 - 50

= 30 units

And the cost of reducing pollution for firm C is equal to $50 per unit. So the total cost of abatement for firm C will be equal to,

= 50 × 30

= $1500

Now the total cost of abatement when the permits aren't tradable will be equal to,

Abatement cost of firm A + abatement cost of firm B + abatement cost of firm C

= $600 + $100 + $1500

= $2200.

So the total cost of abatement when permits are not tradable is equal to $2200.

Now we are given that permits can now be traded.

Let's understand how permit trading can be beneficial for the firms in order to reduce pollution.

Look the cost of reducing pollution for firm A is equal to $30 per unit of pollution so if it can get a permit to pollution at a cost which is lower than $30 per unit then it would be beneficial for firm A to buy permit and let the other firm reduce the pollution.

And as we can see only firm B has a lower cost of reducing pollution than the cost of reducing per unit pollution for firm A and C. And the cost of reducing pollution for firm A and B is higher than the cost of permit so it would be beneficial for firm A and C to buy permits from firm B and let firm B reduce the pollution.

Which firms why how many permits?

See firm A needs to reduce the pollution by 20 units, so firm A will buy 20 permits from firm B at a cost of $20 per permit. And firm A will pollute 70 units of pollution.

The cost of permit to firm A will be equal to,

= 20 × 20

= $400

And similarly firm C needs to reduce the pollution by 30 units so it will 30 permits from firm B. And firm C will pollute 80 units.

The cost of permit to firm C will be equal to,

= 20 × 30

= $600

And now since firm B has sold all his permits so it will reduce its pollution to zero.

So total emission will be equal to,

= pollution by firm A + pollution by firm C

= 70 + 80

= 150 units that's what the aim of the government.

Now the cost of reducing pollution in this case will be equal to the cost of permits that firm A ans C has paid plus the cost of reducing pollution by firm B by 60 units.

The cost of reducing pollution by 60 units for firm B will be equal to,

= 10 × 60

= $600

Now the total cost of abatement will be equal to,

= cost of permit to firm A + cost of permit to firm C + cost of reducing pollution by 60 units for firm B

= 400 + 600 + 600

= $1600.

So the cost of abatement when permits are tradable is equal to $1600.

I hope I was able to help you, if you find this answer helpful please consider giving an upvote. Thank you