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?

Question

Quizplus · Accepted Answer

The Answer of 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?

The Credit River Has Two Polluting Firms on Its Banks