Practice Questions (This is the complete question)

8. Two firms each produce an output of 10 units. The production process for each firm generates 20 units of pollution. Firm 1 can reduce pollution to 11:20 units, where 0 g a: g 1, by inCurring a cost of (1 )200, while firm 2 can achieve the same reduction at a cost of (1 a) 100. Suppose a regulator sets an overall cap at 20 units of pollution and allocates 10 units of pollution rights to each firm. (a) Suppose each firm must reduce pollution to the number of units of allo- cated pollution rights. What is the total cost of reducing pollution to the overall cap of 20 units? [6 marks] (b) If pollution rights could be reallocated across firms in any way, what would be the lowest cost of reducing pollution to the overall cap of 20 units? [6 marks] (c) Suppose the firms can trade pollution rights between themselves, and the price of a unit of pollution right is p. For what values of p would we achieve the lowest cost of reducing pollution as derived in part (b)? [8 marks]