Question

1. A firm’s marginal abatement cost function is given by MAC = 200–5E. Suppose that, after adopting new abatement technology, the firms marginal abatement function becomes MAC = 160–4E. Costs are in dollars per tonne and emissions are in tonnes per year. The firm is given 20 tradeable pollution permits (each permit allows it to emit one tonne of pollution) and the current market price per permit is $100.
a)Given no change in the permit price how many tonnes of pollution will the firm emit?
b)What will be the firms total abatement cost? Will it buy or sell permits and how many?
c) What will be the net cost to the firm after trading? What will be the net gain to the firm from adopting the new abatement technology

Answer 1

1)MAC=160-4*e

100=160-4e

E=60/4=15

The MAC is lower than the permit price,so it better for firm sell permit and reduce pollution and get Profit from it.

So firm will emit 15 tons of pollution.

2) TOTAL ABATEMENT COST=160E-2*E^2

TOtal ABATEMENT COST=160*40-2*40*40 -(160*15-2*15*15)=6400-3200-2400+450=1250

Firm will sell 5 permit in the market .

3)Net cost =total ABATEMENT COST- revenue from selling permit=1250-5*100=1250-500=750

With initial technology,

MAC=200-5*20=100

So marginal abatement cost is equal to permit price ,so firm will neither buy or sell permit.

TAC=200*e-2.5*e^2

TAC=200*40-2.5*40*40 -(200*20-2.5*20*20)=8000-4000-4000+1000=1000

Net benefit from new technology=1000-750=250