Question

1. Below are the marginal abatement costs of two sources: MAC1 = 60Q1 MAC2 = 40Q2 where Q1 and Q2 are, respectively, the amount of emissions reduced by the first and second firms. Assume that with no control at all, each firm would be emitting 60 units of emissions or a total of 120 units for both firms. 1) Compute the cost-effective allocation of control responsibility if a total reduction of 90 units of emissions is necessary. 2) Draw two firms control cost graphs. Label the efficient level of pollution reduction on the graphs.\

Answer 1

MAC1 = 60Q1
MAC2 = 40Q2

For effective clean up, it is necessary to allocate the cost between the two firms => MAC1 = MAC2

This means,

MAC = 60Q1
MAC = 40Q2

Total abatement Q = Q1 + Q2

=> Q = MAC/60 + MAC/40
=> Q = MAC/24

To reduce 90 units of emission:

MAC = 24*Q = 24*90 = 2160

Hence,

Q1 = MAC / 60 = 36
Q2 = MAC / 40 = 54

	Q	5	10	15	20	25	30
60Q1	MAC1	300	600	900	1200	1500	1800
40Q2	MAC2	200	400	600	800	1000	1200

The first 50 units of reduction will be shared in the above way with Firm 2 taking responsibility for 30 units and Firm 1 for 20 units. The next 40 units will be as follows:

	Q	30	36	42	48	54	60
60Q1	MAC1	1800	2160	2520	2880	3240	3600
40Q2	MAC2	1200	1440	1680	1920	2160	2400

The 40 units left will be divided as 16 units for Firm 1 and 20 units for Firm 2

The effective allocation as observed above is shown in a graphical form below:

The intersection point of MAC1 and MAC_opt gives Q1
The intersection point of MAC2 and MAC_opt gives Q2.

Thus from the graph we can see that the efficient level of pollution reduction is given by MAC_opt.

Each firm will continue to abate till the marginal cost of abatement grows to 2160.