Question

1. → Suppose that two firms, X and Y, face the following abatement costs:: 4 MACx=-1.24x MACy=-0.3Ayt TACx=0.6Ax?. TACy = 0.15A7.4 a. Further assume that the combined abatement standard is 40 units for both firms. Based on this model, if the government uses a uniform standard find → the total marginal abatement cost for firm X and Y4 b. → the total abatement cost for firm X and Y4 → the combined total abatement cost for both firms is $1,2004 How much abatement should the government'allocate X and Y in order to achieve minimum use of resources? c.

Answer 1

In this case, Ax=Ay=40

a)

MACx=1.2*Ax=1.2*40=$48

MACy=0.3*Ay=0.3*40=$12

b)

Total abatement Cost for X=0.6*A2=0.6*402=$960

Total abatement Cost for Y=0.15*A2=0.15*402=$240

c)

Combined Total Cost=960+240=$1200

Efficient allocation will require

MACx=MACy

1.2Ax=0.3Ay

Ay=4Ax

We have Ax+Ay=80

Set Ay=4Ax

Ax+4Ax=80

5Ax=80

Ax=16

Ay=4Ax=4*16=64

Efficient allocation requires that firm X should abate 16 units and firm Y should abate 64 units.