Question

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

a.How many units of emissions will the firm abate, what will be its total abatement cost and its total tax bill?
b.How much better off will the firm be if it abates this much compared to if it does not abate at all, given the$110 per unit emissions tax.
c.Suppose that, instead of a $110 per unit emissions tax, the government offers the polluter $110 for each unit of emissions it abates. How many units will the firm abate and what will be its net gain?

Answer 1

In absence of any regulation,

Firm will emit in such a way that MAC=0

i.e. 120-2.5E=0

E=48

If A is abatement level. E=48-A

MAC=120-2.5E=120-2.5*(48-A)=120-120+2.5A=2.5A

a)

Firm will abate in such a way that MAC=Tax rate i.e.

2.5A=110

A=44 units

Firm will abate 44 units of emissions

b)

Total abatement Cost, TAC is given by

Total additional tax if it has not abated=44*110=$4840

Benefit of abatement=4840-2420=$2420

c)

Firm will abate as long as MAC is lower or equal to subsidy rate i.e. $110

2.5A=110

A=44 units

Firm will abate 44 units of emissions

Net gain=Total subsidy amount-TAC=44*110-2420=$2420