Question

​​The Credit River has two polluting firms on its banks. Plants A and B each dump 100 tonnes of effluent into the river each year. The cost per tonne of reducing emissions is $20 for plant A and $100 for Plant B. The government wants to reduce overall pollution from 200 tonnes to 50 tonnes.
a. If the government knew the cost of reduction for each firm, what reductions would it impose in order to achieve its overall goal at the least possible total cost? What would be the cost to each firm, and the total cost?
b. If, in the absence of information about each firm’s costs, the government decided to reach its overall goal by imposing uniform reductions on the firms, what would be the cost to each firm, and the total cost?
c. Compare the total costs in parts a and b. If the government does not know the cost of pollution reduction for each firm, is there still some way to reduce pollution to 50 tonnes at the total cost calculated in part a?

Answer 1

a)

To minimize the total cost of abatement, maximum possible abatement should be done by the firm which has a lower cost of reduction.Since firm A has a lower cost of emission reduction, firm A should be asked to reduce maximum possible reduction for him i.e. 100 tons.

Firm B should be asked to do the rest of the abatement i.e. 50 tons.

Cost of emission reduction for firm A=100*20=$2000

Cost of emission reduction for firm B=50*100=$5000

Total Cost of abatement=2000+5000=$7000

b)

In this case 75 tons of emissions should be reduced by each of the firms.

Cost of emission reduction for firm A=75*20=$1500

Cost of emission reduction for firm B=75*100=$7500

Total Cost of abatement=1500+7500=$9000

c)

Objective of reducing pollution to 50 tons with minimum cost can be done by providing trade able permits. In this system firm with higher cost of abatement i.e. firm B can buy the permits from firm A and total cost of pollution can be minimized.