The Pristine River has two polluting firms on its banks. Acme Industrial and Creative Chemicals each dump 100 tonnes of glop into the river each year. The cost of reducing glop emissions per tonne equals $10 for Acme and $100 for Creative. The local 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 reach its overall goal? What would be the cost to each firm and the total cost to the firms together?

b In a more typical situation, the government would not know the cost of pollution reduction at each firm. If the government decided to reach its overall goal by imposing uniform reductions on the firms, calculate the reduction made by each firm, the cost to each firm and the total cost to the firms together.

c Compare the total cost of pollution reduction in parts

(a) and (b). If the government does not know the cost of reduction for each firm, is there still some way for it to reduce pollution to 50 tonnes at the total cost you calculated in part (a)? Explain.