CON 101: Carbon Tax vs. Cap-and-Trade
The purpose of this page is to describe the differences between a carbon tax and carbon cap-and-trade policies using the most basic of all environmental
economic models.
A Model of a Single Polluting Firm
Consider a polluting firm that faces an increasing marginal pollution abatement cost curve (click on the thumbnail for a larger picture). Left unregulated it
will choose to abate zero units of carbon and avoid the abatement costs represented by the area underneath the marginal abatement cost curve: B + C + D.
Suppose a benefit-cost analysis has determined that optimal abatement occurs at the blue dot where the marginal benefit and marginal cost curves intersect.
The resulting level of emissions is e* (measured right to left along the horizontal axis).
Carbon Tax
One way to achieve this level of abatement is to set a tax where marginal benefit equals marginal abatement cost -- represented by the horizontal "tax" line.
The polluting firm will notice that it is cheaper to abate carbon emissions as long as the marginal abatement cost is lower than the tax. Since the tax bill (A
+ B) is great than the marginal abatement cost bill (B) to the left of the vertical "cap" line the firm will choose to abate. To the right of the "cap" line the
marginal abatement cost bill (C + D) is greater than the tax bill (D) so the firm will choose to pay the tax and continue to pollute.
Results:
•The efficient abatement level is achieved: e*
•The abatement cost to the pollution firm = B + D
•Government revenue = D
Carbon Cap
Another way to achieve this level of abatement is to set a cap where marginal benefit equals marginal abatement cost -- represented by the vertical "cap"
line. The polluting firm must abate its carbon emissions to e*.
Results:
•The efficient abatement level is achieved: e*
•The abatement cost to the pollution firm = B
A Model with Two Polluting Firms
Now things get a bit more hairy. A two-panel diagram is needed to better understand the logic of trading (click the thumbnail for a bigger image). The two-
panel diagram illustrates the increasing marginal abatement costs of two firms. One has an old, dirty, plant with high abatement costs (in blue) that goes
right to left with abatement. The other firm has a newer plant that has lower abatement costs (in green) that goes left to right with abatement. The width of
the horizontal axis is the abatement that must be achieved to reduce overall emissions to the efficient level.
The intersection of the two marginal abatement costs is where economic efficiency is achieved. This is known as the "equimarginal principle." The total costs
of achieving the efficient abatement/emissions level is: C + G + K. The efficient emissions level, e*, shows that the low abatement cost firm should reduce
more emissions than the high abatement cost firm.
Carbon Tax
One way to achieve this level of abatement is to set a tax where the marginal abatement costs are equal -- assuming that we have this information (we don't
but we can iterate towards the intersection) -- represented by the horizontal "tax" line. As above, the polluting firms will notice that it is cheaper to abate
carbon emissions as long as the marginal abatement cost is lower than the tax.
The high cost firm will abate to e* (right to left) and suffer abatement costs of K and pay a tax bill to the government equal to B + C + F + G. The low cost
firm will abate to e* (left to right) and suffer abatement costs of C + G and pay a tax bill to the government equal to J + K.
Results:
•The efficient abatement level is achieved: e*
