Question

Suppose a control authority is trying to design a cost-effective pollution control policy. They assume the aggregate marginal abatement cost is given as MAC = 16 –q and the marginal pollution damage is given as MD = 3q where q is the total amount of emissions. Calculate the socially efficient level of emissions. Use a diagram to explain why the profit-maximising level of emissions and socially efficient level of emissions are different. Suppose the control authority tries to achieve the emission target in part a by using an emission charge system. What per-unit of charge should be imposed? Will this be a cost-effective policy?

d Suppose it is found that the control authorities under-estimated the marginal cost of emission abatement. That is, the true marginal abatement cost is given as MACTRUE =20 – q. Use a diagram to explain what the welfare- loss associated with the per-unit of charge in part c would be.

Answer 1

A) Social efficient emissions is where ,MAC= MD

16-Q=3q

Q=16/4=4

B)

Because MAC shows , marginal profit firm earn by emission. So profit maximizing emissions will be at where MAC=0.

So profit maximizing emiss=16

Social efficient quantity=4

Because firm doesn't take marginal damage to society into consideration , that's why profit maximizing emissions is different than social efficient emissions.

C)The social efficient per unit emissions charge=12( equal to marginal abatement cost st social efficient emission).

Yes ,this cost efficient policy

D) Actual social efficient emissions:

20-Q=3Q

Q=20/4=5

MAC at social efficient emission=20-5=15

So efficient per unit emissions charge=15

With part C) emissions charge , emissions=20-12=8( higher than actual social efficient emission)

MD at Q=8,=3*8=24

Deadweight lose=1/2*(8-5)*(24-12)=0.5*3*12=18