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

[1] Write out the aggregate marginal abatement cost (AMAC) function for the industry. Hint: solve the MAC curves for e and sum them.

[2] Draw a graph with emissions on the horizontal axis and include the MD and AMAC curves.

[3] What is the efficient level of aggregate emissions (E*)? The numeric value, not just the point on the graph.