Question

Suppose there are two sources that cause pollution at a receptor site. Let e denote emissions and q denote abatement, or pollution controlled.

Source	e	MAC
Plant	400	10 qp
Farm	200	10 qF

K ≡ concentration

K = 0.01e_p + 0.02e_F

a. What is concentration level at the receptor site without any abatement?

Suppose the regulatory authority has chosen a target of 5.4.

b. What allocation would achieve this target? Is this a cost-effective allocation?

c. What ambient charge would achieve this target? Is this a cost effective allocation?

d. How would an ambient allowance scheme work in this case?

Answer 1

Here, there are two sources of pollution. The level of total emissions by each and the respective marginal cost of abating the pollution have been given. The concentration level in terms of emissions of both are also given.

Explanation:

a) In case there is no abatement, the level of emission would be maximum, that is 400 units for the plant and 200 units for the farm. The concentration of the receptor site in this situation is,

K = 0.01ep + 0.02ef

K = 0.01 x 400 + 0.02 x 200

K = 4 + 4

K = 8

Thus, the level of concentration at the receptor site would be 8 units.

b) If the target of concentration has been chosen to be K = 5.4 only, that means there is some amount of abatement. So, the level of pollution emitted would be less than the maximum level.

When the equimarginal principle is applied, the MACs are equated to get the cost-effective allocation.

MACp = MACf

10qp = 10qf

That is,

qp = qf = q  

K = 0.01 x (400 - qp) + 0.02 x (200 - qf)

5.4 = 0.01 x (400 - q) + 0.02 x (200 - q)

5.4 = 4 - 0.01q + 4 - 0.02q

5.4 = 8 - 0.03q

0.03q = 8 - 5.4

q = 86.6

Here, the level of abatement by both the firms should be around 86 units. This target would be achieved when the plant and the farm incur marginal cost in an attempt to abate pollution and reduce emissions.

Considering the target given by the regulatory authority, the allocation can be considered cost efficient.

c) Here, the ambient standard refers to the permit price for emitting pollution. Taking the ratios of MAC to the emissions of the respective polluters.

10qp / 400 = 10qf / 200

qp = 2qf

The price of the permit is equal to the marginal cost of abatement.

For plant,

MACp = MACq = 10 x 86.6 = 866 units

To achieve the pollution target at the cost-effective allocation calculated above, the ambient charge for each of the firms would be 866 units.

d) Under the ambience allowance scheme, tradable permits will be issued by the regulatory authority and the total limit on emissions is prescribed. Here, the total amount of emissions would be fixed and if the plant or the farm pollutes less than what is allowed, it can trade permits with the other player but the total emissions should not exceed.