Some Graphs on
Environmental Policy
Raphael Calel
Constructing the Graph
Marginal Abatement Cost
Marginal Social Damage
MSD
MAC
E
E* Emissions
An unregulated firm will produce emissions until the point where there is no
private gain associated with further emissions (E*). When it reduces its
emissions below this point, say to E, it forfeits some of these gains (the
shaded area). The marginal abatement cost is the foregone gain associated
with an additional unit of emissions (the foregone gain can be both profit not
earned because output is reduced, and profit not earned due to investments
in new low-emissions technologies).
The marginal abatement cost curve is drawn as downward sloping. This
reflects that the gain from adding an additional unit of emissions is falling as
emissions increases. Put differently, reducing emission by one unit is more
costly the more we have already reduced our emissions below E*. We can
think of this as resulting from the firm first making the cheapest emissions
reductions, and resorting to more costly abatement options only when it
must reduce emissions further.
For each unit of emissions, society suffers additional damages. The marginal social damage is the additional damage from one extra
unit of emissions. The marginal social damage curve is upward sloping. This reflects that the social damage from one more unit of
emissions is higher when pollution is already high.
Comparing Command & Control with Economic Instruments
Marginal Abatement
Cost
A command & control (C&C) policy sets a uniform emissions standard (E).
When reducing emissions to E, firm 1 will face a marginal abatement cost of
mac1, while firm 2 will face a marginal abatement cost of mac2.
mac1
A
T
B
mac2
MAC1
MAC2
E2
E
E1
Emissions
Economic instruments (e.g emissions tax or emissions trading) provide an
alternative to C&C. Consider a tax on emissions (T), which must be paid for
each unit of emissions. Firm 1 will reduce its emissions to the level E1, where
the marginal abatement cost is just equal to the tax it has to pay. If it emits
more, it is cheaper to reduce emissions than to pay the additional taxes, so it
will reduce its emissions. If it emits less, it is cheaper to increase emissions
(thus reducing abatement cost) and pay the additional taxes. By a similar
argument, firm 2 will want to emit E2.
Suppose that the emissions tax (T) is set so as to achieve the same overall
emissions as the C&C policy (i.e. so that 2E = E1 + E2). Such a tax will exist in
general.
Emissions trading, in this simple model, is equivalent to an emissions tax. Imagine that instead of mandating that every firm can emit
only E, you assign to each firm tradeable permits to the amount E. Firm 1 then faces a higher marginal abatement cost than firm 2.
If firm 1 offers to pay firm 2 somewhere between mac1 and mac2 for an emissions permit, firm 2 would do well to sell the permit,
because he receives more in payment than it costs him to reduce his emissions. As long as the firms have different marginal
abatement costs, they can find such opportunities for mutually beneficial trade. No more such opportunities will exist only when
marginal abatement costs are equal (in which case they will also both be equal to T).
Let us now compare C&C with economic instruments. Imagine that the price of a permit is T from the beginning. Firm 1 then wants
to buy permits to allow him to increase emissions up to E1. In order to do this, he must pay T x (E1 - E), but his benefit from
increasing his emissions is equal to the whole area under MAC1 between E and E1. Hence, he makes a net gain of the shaded area A.
At price T, firm 2 wants to sell permits so that he ends up at E2. By selling his excess permits, he gets T x (E -E2), but the cost of
reducing his emissions is equal to just the area under MAC2 between E2 and E. Hence, he makes a net gain of the shaded area B.
Therefore, in the case of emissions trading (or, equivalently, a tax), both firms make a net gain compared to the C&C policy, while the
same level of overall emissions is achieved in both cases. Economic instruments allow us to achieve the same emissions reductions at
a lower cost.
Incentives to Innovate
Marginal Abatement
Cost
The firm’s marginal abatement cost curve is initially given by MAC. Suppose
now that the firm can invest in inventing a new technology that is cleaner.
With this new technology, the firm needs less emissions to produce a given
amount of output, so the marginal abatement cost is lower at each level of
emissions below E*. The new marginal abatement cost curve is MAC´ How
much will the firm be willing to invest in innovation?
MAC
MAC´
T
mac´
B
A
Consider first a C&C policy, which allows the firm to emit only E. If the firm
invents the new technology, it continues to emit E, but now faces a marginal
abatement cost of only mac´. The total reduction in abatement cost is equal
to the difference in the areas beneath MAC and MAC´, which is given by the
shaded area A. Because the firm can gains A pounds by having this new
technology, they will be willing to invest at most A pounds to invent it.
Consider now an emissions trading scheme with the permit price at T (or,
equivalently, a tax of T), so the firm will choose to emit E. If the firm invents
E´
E
E* Emissions
the new technology, it will face a marginal abatement cost of only mac´ at
this level of emissions. Because mac´ is lower than T, the firm earns more by
selling an emissions permit and reducing his emissions. It is profitable to continue selling permits and reducing his emissions until his
marginal abatement cost is equal to the permit price T. At this point, the firm will only be emitting E´ units, which is less than E.
How much has it gained by inventing the new technology? The total reduction in abatement cost at the initial level of emissions is
equal to A. In addition, the firm has now earned an extra T x (E - E´) by selling emissions permits, while only incurring an added cost
of the area under MAC´ between E´ and E. The firm has thus made an extra gain equal to the shaded area B. The total gain from
innovation is A+B. The firm would therefore be willing to invest at most A+B pounds to invent the new technology.
Let us now compare the C&C with economic instruments. With a C&C policy, the firm is willing to invest only A pounds to invent
new cleaner technologies, while with economic instruments, the firm is willing to invest A+B pounds. Also, when the technology is
finally invented, emissions remain at the level E with a C&C policy, while they fall to E´ with economic instruments. Economic
instruments then give greater incentives to invent new cleaner technologies, and reduces emissions more once the new technologies
are invented.
Comparing an Emissions Tax with Emissions Trading
Marginal Abatement Cost
Marginal Social Damage
MSD
T´´
T
A
B
T´
MAC´
MAC
MAC´
E´
E
E´´
Emissions
So far, emissions taxes and emissions trading have been equivalent in our
model. However, this is only true if we know the marginal abatement cost
curve of each firm when we set the the tax or emissions allowance. If we do
not know the positions of these curves, an emissions tax and emissions
trading will no longer be equivalent.
Consider first an emissions tax. Let us guess that the firm faces the marginal
abatement cost curve MAC´, and as a result we will want to set the tax T´.
The true marginal abatement cost curve, however, is MAC. The firm will then
want to emit E´´. Had we known the true marginal abatement cost curve, we
would instead have set the tax T, and the firm would have wanted to emit E.
For each unit of emissions above E, the marginal social damage exceeds the
marginal abatement cost, so there is a net welfare loss. The total welfare loss
from our incorrect guess is then given by the shaded area A. Suppose we
instead overestimated the firm’s marginal abatement costs and guessed MAC
´´, and consequently set the tax to T´´. By a similar argument as before, the
firm would emit E´, and the total welfare loss would be equal to the shaded
area B.
Consider now an emissions trading scheme with an emissions allowance of E. For simplicity, there is only one firm in this scheme, so
it cannot buy or sell permits (if it helps, think of this firm as the entire economy, and E as the economy-wide emissions allowance).
Suppose we guess that the firm faces MAC´, and as a consequence allow the firm to emit only E´. The firm will then face a marginal
abatement cost of T´´. Had we know the true marginal abatement cost curve, we would have allowed the firm to emit E, and it
would face a marginal abatement cost of only T. For each unit of emissions below E, the firm pays more to abate than the value to
society of reduced emissions, so there is a net welfare loss. The total welfare loss from our incorrect guess is then given by the
shaded area B. Suppose we instead overestimated the firm’s marginal abatement cost curve and guessed MAC´´, and consequently
allowed the firm to emit E´´units. By a similar argument as above, the firm would face a marginal abatement cost T´, and the total
welfare loss would be equal to the shaded area A. In the above graph, the expected welfare losses of guessing wrong is the same with
an emissions tax and with emissions trading. However, this is not true in general. To see this, try to draw the graph first with
relatively steep MAC curves, and you will find that the welfare loss of a small error in guessing is smaller with emissions taxes than
with emissions trading. Try then to draw the graph with relatively shallow MAC curves, and you will find that emissions trading is
better.