Question

Is this statement true or false? Explain why the statement is true or false.

Two firms, 1 and 2, can control their emissions of a pollutant according to the following marginal cost equations: MC₁ = $1*q₁ and MC₂ = $1/2*q₂, where q₁ and q₂ are the amount of emissions controlled by firm 1 and firm 2, respectively. In addition, each firm is currently emitting 100 units of pollution and neither firm is controlling its emissions. Assuming the control authority has concluded that the total emissions generated by the two firms must be reduced by 60 units. The cost-effective allocation in reduction is to have firm 1 reduce emissions by 40units and firm 2 reduce emissions by 20 units.

Answer 1

The statement is true.

Explanation:

Two firms abatement ratio = MC₁ : MC₂

                 1q₁ : (1/2)q₂

              i.e 1 : 0.5

            Total = 1 + 0.5 = 1.5

Total Emission must be reduced by 60 units.

i.e 60 / 1.5 = 40 units

Firm 1 have to reduce emissions by = 40 units * 1 = 40 units

Firm 2 have to reduce emissions by = 40 units * 0.5 = 20 units