Assume you have three firms with different marginal abatement cost functions as follows: MAC1 =2q1
MAC2 =q2 MAC3 = 12q3
It has been determined that the total amount of pollution should be reduced by 35 units.
(a) Find the cost-effective allocation of pollution abatement for each firm.
From the MAC function for cost effective allocation MAC1=2MAC2=MAC3/6, now for 3rd first unit of abatement cost=12*1=$12 and at or below same MAC second firm can abate 12 units while first can abate 12/2=6 units so Total units abated =12+6+1=19 units now remaining=35-19=16 units of which 11 units will be second firm and first will abate 5 since third firms cost is $24(12*2) for 2 nd unit which is higher than (12+11)=23rd units abatement cost of $23 Henec, cost effective way is to abate 23 units from second firm,(6+5)=11 units from first firm and 1 unit from 3rd firm.
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