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Efficiency through Emissions Taxes Consider two firms that emit a uniformly mixed air pollutant (e.g., carbon...

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 - 2e1

MAC2 = 100 - 0.50e2

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.

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Answer #1

1) e1 = (100-MAC)/2

= 50-.5MAC

e2 = (100-MAC)/.5

= 200 - 2MAC

Then Aggregate MAC :

E = e1+e2

E= 250 - 2.5MAC

MAC = (250-E)/2.5

MAC = 100 - .4E

2) MD = .4E

3) at eqm,

MAC = MD

100-.4E = .4E

100 = .8E

E* = 100/.8 = 125

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