Question

18. 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 situation? (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? [ Parts (a), (b) and (c) aren't related to one another]

Answer 1

a). Consider the given problem here the marginal abatement cost and marginal damage functions are given by.

=> MAC = 36 – 2*E, and MD = E. If the tax rate on emission of $9/unit, => at the equilibrium MAC must be equal to tax rate.

=> MAC = t, => 36 – 2*E = 9, => 2*E = 27, => E = 27/2 = 13.5, => E1 = 13.5.

The level of emission is “E1 = 13.5”.

Now, under the zero tax situation the polluter will pollute until the MAC is zero, => MAC = 0.

=> MAC = 0, => 36 – 2*E = 0, => E = 36/2 = 18 units. So, without any restriction the firm will emit such that the MAC is zero, => the corresponding level of emission is 18 units.

The compliance cost is given by, => 0.5*(18-13.5)*9 = $20.25.

b).

At the socially optimum level the MAC must be equal to MD.

=> MAC = MD, => 36 – 2*E = E, => 3*E = 36, => E = 12 units. So, the socially efficient tax rate is “MD = E = $12 per unit”.

c).

If the polluter bargains to pay $6 for each unit of emission then at the optimum the following condition holds.

=> MAC = 6, => 36 – 2*E = 6, => E = 30/2 = 15 units.

So, cost of reducing pollution from 18 units to 15 units is given below.

=> Total cost = 0.5*(18-15)*6 = $9, => the cost decreases to $9, => the net gains is “20.25 – 9 = $11.25”.