Question

Suppose there are two firms: Firm A and Firm B. These firms are each emitting 50 tons of pollution. Firm A faces marginal abatement cost MACA = 6A and Firm B faces marginal abatement cost MACB = 12A where A is tons of pollution abatement. The government wishes for the total amount of pollution to be 80 tons.

1. (2 points) At the cost effective allocation of abatement, how much does Firm A abate?

2. (2 points) What tax per ton of pollution would result the cost effective allocation of abatement?

3. (1.5 points) What is the total cost of abatement if the government implements the tax you solved for in question 5?

Answer 1

Abatement needed = 20 tons because pollution should reduce from 100 tons in total to 80 tons

We must have MACA = MACB for cost effective allocation

6A1 = 12A2 or A1 = 2A2. We now have A1 + A2 = 20 so 2A2 + A2 = 20 and A2 = 20/3 = 6.67 while A1 = 13.33

A tax should be placed such that cost effective allocation is reached

Find aggregate MAC

A1 = MACA/6 and A2 = MACA/12

A1 + A2 = 3MAC/12

20 = MAC/4

MAC = tax = $80

This gives an appropriate tax per ton = $80.

Total cost of abatement by firm A = (Area under the MAC curve) = 13.33*80*0.5 = 533.2 and for firm B = 6.67*80*0.5 = 266.8. Total cost of abatement = 800.