Question

There are two firms producing cement. Each produces 20 units of pollution, and each has the ability to reduce pollution (abate) their emissions by operating some machine. The marginal damage of each unit of pollution to society is $3 (i.e., the marginal benefit of each unit of abatement is $3). The total cost of firm 1 is $LaTeX: \mathcal{C}^1=\frac{1}{6}a_1^2$ where denotes the amount of abatement of firm 1. The total cost of firm 2 is $LaTeX: \mathcal{C}^2=\frac{1}{4}a_2^2$ where denotes the amount of abatement of firm 2. Suppose that the government gives each business a permit allowing them to emit 12.5 units (instead of 20). The permits are not tradable. This will create 15 total units of abatement, adding up across both firms.

Question: What is the cost of achieving this level of abatement?

Answer 1

a)

Under the regulation

Abatement required for firm 1=Emission without regulation-allowed pollution limit

Abatement required for firm 1=20-12.5=7.5 units

Total cost of abating 7.5 units of pollution for firm 1 is

C¹=1/6*(7.5)²=9.375

Abatement required for firm 2=Emission without regulation-allowed pollution limit

Abatement required for firm 2=20-12.5=7.5 units

Total cost of abating 7.5 units of pollution for firm 2 is

C²=1/4*(7.5)²=$14.0625

Total Cost=C¹+C²=9.375+14.0625=$23.4375