Topic 2: Production Externalities
•
NB = CS + PS - EC + REV
c
New MPC
= MEC
12
MPC (S)
9
8
E
6
C
F
J
H
EC = areas H+E
= $9,000
Recall that without the
tax EC = H+E+C+F+J
= $12,000
3
MB
300
400
Q
1,200 (thousands kwh)
EC decrease by areas C+F+J = $3,000
Less output  less pollution  fewer environmental costs
Note: Efficient emissions ≠0!
1
Topic 2: Production Externalities
•
NB = CS + PS - EC + REV
c
REV = areas B+D+E
= $9,000
New MPC
= MEC
12
MPC (S)
9
8
6
Without the tax REV = 0
(obviously)
B
D
E
 Tax-payers gain $9,000.
3
MB
300
400
Note that REV = t  Q
= MEC  Q
Recall that EC = MEC  Q
(because MEC is constant in Q)
Q
1,200 (thousands kwh)
 REV = EC
2
Topic 2: Production Externalities
Combined gains in terms of EC and REV:
c
New MPC
= MEC
12
MPC (S)
9
8
6
B
D
E
C
F
J
EC + REV
= areas B+C+D+E+F+J
= $3,000 + $9,000
= $12,000
3
MB
300
400
Recall: combined losses to CS
and PS were
= B+C+D+E+F
= $10,500.
Q
1,200 (thousands kwh)
Gains exceed losses by
$1,500 = J.
Area J was DWL.
3
Topic 2: Production Externalities
•
•
•
•
Summary of effects of per unit tax on output:
If we set t = MEC:
– The efficient Q is achieved.
– Losses in terms of CS and PS
– Gains in terms of REV and EC
Gains > Losses  NB
Relevant question for policy:
What information does the environmental regulator need in
order to be able to implement this policy?
– If MEC is constant in Q, then we just need to know what
that MEC is equal to.
– No requirement to know MPC or MB (demand).
4
Topic 2: Production Externalities
•
•
•
Exercise (more difficult):
Suppose we have the same MB and same MPC curves as
in the previous example, but now suppose that MEC =
(1/100)Q (that is, as Q , MEC ).
Questions:
1. What is the efficient level of output? Draw a diagram.
2. Calculate the DWL that results at the equilibrium if there
is no policy to correct the market failure.
3. If the government wishes to correct the market failure by
setting a constant per unit output tax, what will that tax
need to be?
4. Calculate the CS, PS, EC, REV as result of this
tax.
5. What new information does the regulator need in this
case (relative to the case of constant MEC) in order to
achieve efficiency?
5
Topic 2: Production Externalities
2.
Quota on production
•
Now suppose we want to achieve efficiency, but
through a quota on production rather than a per unit
output tax.
If we limit output per power plant to 3,000 kwh, then
aggregate Q cannot exceed 300,000 (the efficient Q).
•
•
Questions:
– What is the new equilibrium P and Q?
– Who gains and who loses as a result of the quota?
– What information does the regulator need in order to
achieve the efficient Q?
6
Topic 2: Production Externalities
Effect of a quota on the market for electricity:
c
MEC
12
MPC
9
8
If aggregate Q cannot
exceed 300, then P to
$0.09.
Effect on CS identical to
effect of t=$0.03.
3
MB
300
400
Q
1,200 (thousands kwh)
Effect on EC identical to effect of t=$0.03.
What about PS? Exercise: Calculate the PS and show
that PS + EC > CS by an amount equal to the initial
DWL. Also, what information does the regulator need in
7
this case?
Topic 2: Production Externalities
3.
•
•
Per unit subsidy on output reduction.
Finally, suppose we want to achieve efficiency, but by
paying producers to reduce their output.
Key point to understand:
– A subsidy on Q increases the firm’s MPC in (more
or less) the same way a tax does.
– The subsidy increases the opportunity cost to the
firm.
• If the firm decides to produce an extra unit of Q,
the firm must pay its MPC, but now must also
forgo the subsidy.
8
Topic 2: Production Externalities
•
•
•
In our example, each firm chooses Q = 4,000 with no
regulation.
Suppose the govt offers to pay each firm $0.03 for
every unit it doesn’t produce, below the baseline output
of Q = 4,000.
Example: if a firm chooses Q = 3,800, it receives the
subsidy on 200 units (i.e., it receives a payment of
$6.00), etc.
9
Topic 2: Production Externalities
Effect on an individual firm of a subsidy on Q reduction:
c
MPC with sub on Q
MSC
MPC
Govt pays firm $0.03 per
kwh not produced below
4000.
MPC for all Q < 4,000.
3
4
If Q < 4,000, the cost to the firm of an extra Q
= MPC + subsidy forgone
= MPC + $0.03
= MSC
Q
(thousands kwh)
10
Topic 2: Production Externalities
Effect on electricity market of a subsidy on Q reduction:
c
MSC
12
9
New equilibrium is at Q =
300, with consumers
paying P =$0.09 per unit.
MPC
Effect on CS and EC
will be the same as
with the tax and quota.
3
MB
300
400
Q
(thousands kwh)
Exercise: By how much does PS? How much does REV?
Identify the areas corresponding to PS & REV. Show that
PS + EC > CS + REV by an amount equal to the initial
DWL. What info does the regulator need in this case?
11