PIGOUVIAN TAXES

1
PIGOUVIAN TAXES

• ENVIRONMENTAL ECONOMICS
• (part 2)

Dr. Fidel Gonzalez Department of Economics and
Intl. Business Sam Houston State University
2

• The analysis of the previous set of slides has a
  lot of assumptions, many of which are not very
  realistic
• Fixed pollution per unit of output of the good.
• An omniscient government (the govt, knows all).
• All the perfect assumptions hold.
• Many identical agents.
• No administrative costs.

3
Assumption 1 Fixed pollution per unit of output
of the good. In the graphs used to calculate the
consumer and the producer surplus, the victims
and government revenue the amount of the good was
on let x-axis and its price on the
y-axis. Pollution was not represented in any
axis. However, we were able to say that reducing
the output of the good was similar to reducing
pollution because the level of emissions was a
fixed proportion of the output. If output is Q,
emissions E, then we assumed that Q c E
where c is just a constant. Each unit of
production of steel generate emission by c. For
instance if c2 and Q100, then E50. When Q goes
up by one unit Q101, E50.5. Q and E move not
only in the same direction but also at a fixed
change. Hence, placing a tax on Q is similar to
placing the tax on E.
4
(No Transcript)
5
Imagine the government wants to tax emissions in
5 per unit of emissions. Using our previous
information, the government can set a tax of the
production of steel as follows
6
Two-part Instrument

• When the emissions per unit or output are not
  fixed the pigouvian tax has two effects
• Substitution effect
• The production of a good Q uses inputs such as
  labor, capital and natural resources. We can say
  that
• Qf(L,K,NR) this generate pollution so that
  emissions and output are a function of the
  inputs.
• (Q,Emissions)f(L,K,NR)
• An alternative way to see this is by considering
  emissions an input to the production of Q. That
  is, in order to produce Q we need to emit certain
  amount. Now, we can write the previous equation
  as follows
• Q f(L, K, NR, Emissions)
• The amount of L,K, NR and Emissions that the firm
  will use to produce Q will depend in the
  technology of the firm and the price of each
  input.

7
Two-part Instrument
For simplicity imagine that the firm has only two
inputs Labor and Emissions. Then I can graph all
the possible combinations of L and Emissions that
can give me the same amount of Q.
L
Before the pollution tax, the price of emissions
is zero (it is free to pollute). At that point
the firm chooses a combination of inputs La and
Ea.
B
Lb
A
La
Q
Eb
Ea
Emissions
After the pigouvian tax, pollution is more
expensive so the firm substitutes some emissions
for labor. You can see this as the hiring more
labor to abate emissions because now they have to
pay for emissions. This is the substitution
effect of the pigouvian tax.
8
Two-part Instrument
Output Effect
In the substitution effect the amount of output
produce is unchanged. However, the pigouvian tax
increases the cost of production. When costs
increase output decreases. The ouput effect of
the pigouvian tax is to decrease output.
Since we now know how the pigouvian tax affects
firms, we can simulate it using a two-part
instrument. We can obtain the substitution effect
by subsidizing labor, that makes emissions more
expensive compared to labor. The output effect we
can get it by taxing output, that reduces the
amount of output. The advantage of the two-part
instrument over the pigouvian tax is that the
former takes place over market transaction that
are easy to monitor.
9
Assumption 2 An omniscient government (the govt,
knows all).
The government knows everything about the
consumers, producers, victims and pollution. The
government knows what is the private marginal
cost, social marginal cost, private marginal
benefit, marginal pollution damages. In
addition, the government needs to know what is
the MPD at the social optimum level. Why? I did
not mention this before but the pollution tax
has to be equal to the marginal pollution damages
at the social optimum level. In the example we
used before the MPD was always the same so we
implicitly did it. In order to show this
consider the following graph
10
Imagine we have the situation of the graph in the
left. In order for the Pigouvian tax to produce
the optimal solution has to move the MC curve to
the left in such a way that the market
equilibrium is equal to the social optimal level.
PMC tax
SMC
P
P
PMC
Po
Pm
PMBSMBD
Qo
Qm
Q
Q
In order for the market supply to move enough so
that PMC taxSMCPMBSMB the supply curve has
to shift by the MPD at the socially optimum (the
green line in the graph).
11
Imagine that you set the taxMPD for quantities
above the social optimum level. Note how the
setting a tax higher than the MPD at the social
optimum will not produce the social optimum
solution
PMC tax
SMC
P
PMC
P
PMBSMBD
Q
Q
If the tax is higher than the MPD at the optimum,
the supply will shift to the left more than the
necessary amount. Hence the quantity will be less
than the social optimum and the price will be
higher.
12
If the tax is lower than the MPD at the optimum,
the supply will shift to the left less than the
necessary amount. Hence the quantity will be more
than the social optimum and the price will be
lower.
SMC
P
PMC tax
PMC
P
PMBSMBD
Q
Q
13
Assumption 3 All perfect assumptions hold

• Perfect competition the market is perfectly
  competitive, there are many consumers and sellers
  and nobody has market power. If a seller or
  consumer has market power then the graph used
  before does not apply.
• Perfect information consumers and sellers have
  perfect information about the market. Also, the
  victims of pollution have perfect information
  about the pollution damages.
• Perfect Certainty there is no uncertainty,
  consumers, producers, victims and government have
  no uncertainty about the market, everything is
  known with certainty.
• Perfect Mobility all the factors move according
  to the prices perfectly so that there is no
  unemployment.
• Perfect mixing everyone receives the same amount
  of pollution.

14
Assumption 4Many identical agents
All agents are identical in the sense that
pollution affects them in the same way. Hence,
all agents share the welfare gain of the tax in
the same way. If this is not true then some
people will be better off and some people will be
worse off, and therefore it will not be a Pareto
improvement (it will not be efficient).
Assumption 5 No administrative costs
Administrative costs reduce the welfare gain of
the policy. If the administrative burden (cost)
is higher than the welfare gain then in the net
the policy will reduce welfare. Hence, for the
Pigouvian tax to be efficient we need to have a
no administrative cost or than these costs are
less than the welfare gain.