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**

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