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Homework answers / question archive / Two polluting firms can control emissions of a pollutant by incurring the following marginal abatement costs: MAC1 = $300 - 10E1 and MAC2 = $90 - 5E2
Two polluting firms can control emissions of a pollutant by incurring the following marginal abatement costs: MAC1 = $300 - 10E1 and MAC2 = $90 - 5E2. Assume the target level of pollution is 30 units. We do not know if this is the socially efficient level.
A. Compute the level of emissions per firm that is cost effective.
B. Assume a regulator initially assigns 15 permits to each polluter. The government provides these permits to the firms without charge. Given the existence of a transferable discharge permit market, solve for the number of permits each firm will hold, the price of a permit, and the total cost savings to society generated by this market.
A.
The target level of pollution is 30 units, so
E1+E2=30unitsMAC1= 300−10E1MAC2= 90−5(30−E1)E1+E2=30unitsMAC1= 300−10E1MAC2= 90−5(30−E1)
The abatement cost is minimize at:
MAC1=MAC2300−10E1=90−5(30−E1)360=15E1E1=24E2=6MAC1=MAC2300−10E1=90−5(30−E1)360=15E1E1=24E2=6
Hence, the level of emissions per firm that is cost effective is E1 = 24 and E2 = 6.
B.
The assign permits is 15 to each polluter and the pollution emit by firm 1 is 24 and firm 2 is 6. So, firm 1 will trade 9 units of permits to firm1. The price of the permits offer by firm 1 will be:
Should be MAC1=300−10(15)=150Actually MAC1=300−10(24)=60Should be MAC1=300−10(15)=150Actually MAC1=300−10(24)=60
The difference between actual and should be marginal cost will the price offered by firm1, which is 90.
The least amount accepted by firm 2 will be (60 - 15) =& 45.
Can be MAC2=90−5(15)=15Actually MAC2=90−5(6)=60Can be MAC2=90−5(15)=15Actually MAC2=90−5(6)=60
If Firm 2 sells all of its permits at $90, its MAC2 is $90 and it receives $90 from the sale of permits so effectively it is better off. Hence firm 2 will sell 15 permits for $90, each permit for 6. Firm 1 has a MAC of 0 but pays $90 in buying permits. Initially,
Total MAC=60+60= 120Total MAC=60+60= 120
After the permit transfer;
cost saving=120−90=30cost saving=120−90=30
The total cost savings to society generated by this market is $30.
