Question

Two firms can control the emissions of a pollutant by incurring the following marginal abatement cost and total abatement cost.

Firm 1: MAC_1=300−10E_1 TAC_1=300E_1−5E_1^2

Firm 2: MAC_2=90−5E_2 TAC_2=90E_2−2.5E_2^2

Assume that the current target level of pollution is 30 units (total) under a standard. We do not know if this is the socially efficient level or not. Each firm is limited to 15 units each.

The government is debating a levying a unit tax. However, it does not know what it should set the tax rate at, such that, in total, 30 units of pollution are still produced for the whole region. Answering the following questions will help you.

1. [4 points] find the tax rate such that abatement by the firms is total at 30.

2. [2 points] find each firms total abatement cost (TAC) at that found tax rate.

3. [1 point] find the tax payment by each firm.

4. [3 points] what issues should the government worry about when switching from a standard to a emission charge? (logistic problems of implementing such policy)

Answer 1

To find the tax rate that results in 30 units of total abatement, we need to find the point at which the marginal abatement cost (MAC) of both firms are equal, and the sum of their emissions adds up to 30.
Setting the MAC of both firms equal,
300 - 10E1 = 90 - 5E2
Solving for E1 and E2,
20 = E1 = E2
Since both firms are limited to 15 units each,
E1 + E2 = 30
Therefore, the tax rate should be set at 20 - 15 = 5.
At the tax rate of 5,
E1 = 20 - 5 = 15
E2 = 20 - 5 = 15
So the TAC of firm 1 is
TAC1 = 300 * 15 - 5 * 15^2 = 2250
And the TAC of firm 2 is
TAC2 = 90 * 15 - 2.5 * 15^2 = 975
The tax payment of each firm can be calculated as
Tax payment for firm 1 = 5 * 15 = 75
Tax payment for firm 2 = 5 * 15 = 75
When switching from a standard to an emission charge, the government needs to worry about several issues:
Ensure that all firms are aware of the new policy and understand how it affects their operations
Set up a system to monitor and enforce the new policy
Ensure that the tax rate is set correctly to achieve the desired reduction in pollution
Consider the distributional effects of the policy, such as how it affects different firms and industries differently
Address any potential concerns about the fairness and equity of the policy.