Question

Suppose a firm’s marginal abatement function is given by MAC = 120 –2.5E, and it faces a $110 per unit emissions tax. Suppose damages caused by this firm’s pollution is given by the function MD = 5E.

a) To achieve social efficiency, how many units of emissions should the firm abate?
b) What size per unit tax will give the firm an incentive to abate to the socially efficient level of emissions?
c) If the firm abates to the socially efficient level of emissions, what will be the social compliance cost and the private compliance cost of the per unit tax in?

Answer 1

ANSWER:

GIVEN THAT:

THE FIRMS MARGINAL ABATEMENT FUNCTION IS GIVEN BY MAC=120-2.5E

A.

TO ACHIEVE SOCIAL EFFICIENCY:

1. To achieve social efficiency, MAD should be equal to MD. This is because if MD or damage to environment is > abatement costs, then there exists negative externality. So if taxes are imposed to correct negative externality then firms will find it it cheaper to abate pollution.

2. Further if abatement costs > damage done then firms will not be willing to cut emissions.

Therefore optimal level of emissions is -

120 -2.5E = 5E

or,

E = 16.

B.

THE SIZE PER UNIT TAX WILL GIVE THE FIRM:

1. Current per unit tax on emissions is $110 , when Marginal Damage is only 80.

Note :

On substituting 16 in MD equation, we get MD =80

Therefore in order to ensure that firms comply to abatement, per unit tax should be equal to where; T =MAC =MD , This $80 per unit emission.

C.

THE FIRM ABATES TO THE SOCIALLY EFFICIENT LEVEL OF EMISSIONS:

1. Social compliance cost is the tax which polluting firms have to pay for complying to emissions standards.

2. This is $80×16=$1280

Private compliance cost is the total abatement costs of the emissions. 120×16+ 2.5×16×16 = 1280.