Question

A firm’s marginal abatement cost function is given by MAC = 200–5E. 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. Suppose that, after adopting new abatement technology, the firms marginal abatement function becomes MAC = 160–4E

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

a. Permits are a benefit for the firm, for every permit sold in the market, the firm gains $100. Hence 100 is the marginal abatement benefit.

The firm will produce at : MAC = MAB

200 - 5E = 100

E = 20

b. Firm's total abatement cost will be calculated by integrating the MAC function.

TAC = 200E - 2.5E2

Since, the number of emissions from part a are 20, the firm would neither by or sell the permits because it has 20 permits already.

c. Since, the firm does not trade, the net cost does not change.

After, technological improvement, MAC = 160 -4E

New emission count is,

160 - 4E = 100

E = 15

Since, the firm will now emit only 15 units, it can sell 5 units of permit and earn 100*5 = $500.

Technological improvement leads to a net gain of $500.