Question

Efficiency through Emissions Taxes

Consider two firms that emit a uniformly mixed air pollutant (e.g., carbon dioxide).

The marginal abatement cost functions for Firm 1 and Firm 2 are (subscripts indicate firms):

MAC₁ =  100 - 2_e1

MAC₂ = 100 - 0.50_e2

Aggregate emissions for the industry are denoted as E = e₁ + e₂.

The marginal damage function is:

MD = 0.40E

[4] What is the efficient level of emissions for the two individual firms?

e₁^* =

e₂^* =

[5] What should the regulator choose for an emissions tax to achieve efficiency?

[6] Under the tax you answered for Question [5] what is the total abatement cost for each firm?

TAC₁(e₁^*) =

TAC₂(e₂^*) =

[7] Under the tax you answered for Question [5] what is the total amount of taxes paid by each firm?

TAC₁(e₁^*) =

TAC₂(e₂^*) =

Answer 1

The marginal damage function is a key ingredient to normative policy analysis. When the marginal abatement cost equal to marginal damage that is, 0.4E = 100-2E1 for the firm 1. when 0.4E= 100-0.50e2 for the firm 2. The change in the damages per unit of pollutants from emission should be calculated.Relevant government taxation can solve the problem to a certain extent. The firm or industry will try to reduce the pollution due to the increase in taxes which they have to pay as a social cost.