Suppose there are two factories that are currently emitting some undesirable pol

Question

Suppose there are two factories that are currently emitting some undesirable pollutant into the air. Factory one has marginal abatement cost of MAC1 = 500 - 5e1 and factory two has marginal abatement cost of MAC2 = 1500 - 15e2, where e represents the level of emissions for each firm. Suppose the government wants to reduce emissions so that the total emissions equal 120, or e1 + e2 = 120. Enter whole numbers in each blank.

To minimize the total cost of achieving this reduction in emissions, firm 1 should have emissions equal _______ to  and firm 2 should have emissions equal to ______ . At these levels of emissions, the marginal abatement cost for firm 1 is $______ and the marginal abatement cost for firm 2 is $_____. The total abatement cost for firm 1 is $________ and the total abatement cost for firm 2 is $_______.

Explanation / Answer

0r 500-e1-1500+15(120-e1)=0 0r 500-e1-1500+15*120-15e1=0 0r 16e1=15*120-1500+500 Or 16e1= 800 0r e1=800/16 50 or e2=120-50 70 MAC1=500-5*50 250 MAC2=1500-15*70 450 Total Abatement cost for firm1 500 Total Abatement cost for firm2 1500

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