Question

Suppose a community faces a pollution problem because of emissions from a polluter with MAC=36- 2E. The information on pollution damages is given by MD=E .
(a) If there is a tax rate on emissions of $ 9/unit, then what is the emission level choosen by the polluter in equilibrium? What is the amount of its compliance costs?
(b) What is the socially efficient tax rate in the given situaton?
(c) Now imagine a situation where the polluter bargains with the community ( let's say, with the community government) and offers to pay $6 for each unit of emission ( i.e. $6/unit) it is allowed to produce. What level of emissions is the community likely to allow? What is the likely net gain to the community from allowing those units of emissions?

Answer 1

a) When the tax rate on emissions is $ 9/unit, the marginal abatement cost can be modified as

MAC = 36 - 2E - 9 = 25 - 2E

This is because for every unit of emission you reduce, you gain $9 in saved taxes and hence, this is subtracted from the abatement cost.

Firm minimizes total abatement cost with respect to E by equating MAC = 0

i.e. E = 12.5 units.

When there is a tax rate on emissions of $ 9/unit, emission level choosen by the polluter in equilibrium is 12.5 units.

Compliance cost is simply given by amount paid in tax = 12.5*9 = 112.5

(b) Socially efficient emission level is given by MD=MAC

E=36 - 2E

E = 36/3 = 12

Therefore, ocially efficient emission level is 12 units

Let the tax rate required to acheive this be t

MAC = 36 - 2E - t

Firm minimizes total abatement cost with respect to E by equating MAC = 0

i.e. 36 - 2E - t = 0

Socially optimal emission level is E = 12

For this, tax rate t must be such that 36 - 2*12 = t

i.e. t = $12

Therefore, socially efficient tax rate is $12/unit.

(c) If the polluter pays $6 to the community for every unit of pollution, MD is now modified to be E - 6. Community minimizes TD which is at MD = 0 i.e. E = 6. Therefore, community allows 6 units of emission when paid $6/unit of emission.

Gain in payment from firm = 6E = 6*6 = 36

Loss due to emissions = E² = 6*6

Net gain of the community = 36 - 36 = 0