Regulating a Natural Monopoly
Natural Monopoly = A firm whose LRATC curve is downward sloping over the relevant range
of output.
That is, as Q increases, LRATC continues to fall. An example would be a power company like
CPS. If they add one more customer, their total cost will not increase very much. The big costs
for CPS are the power plants, trucks, workers, etc. Adding one more customer only requires a
few lines and some time by the work crew. As they add more customers (or Q increases), they
spread the big costs of things like the power plant over more and more customers.
Recall that
ATC = TC/Q
So if Q keeps rising and TC does not go up much, ATC will fall. This is called economies of
scale. Recall also that economies of scale is considered a barrier to entry. Let’s see why.
The graph below shows the LRATC for a natural monopoly. As Q increases, LRATC falls.
P,C
LRATC
D
Q
This actually keeps competitors out. Why? Suppose that we have one firm in this industry
already, the “old firm (O).” Since they have been in the industry for a long time, their sales (Q)
will be high. So their ATC will be low.
If a “new firm (N)” tries to enter, their ATC will be will be high because, as a new firm, they
will not have high sales (Q).
P,C
ATCN
ATCO
LRATC
D
QN
QO
Q
To make a profit (or at least avoid losing money), a firm needs P > ATC. But the new firm will
always have a higher ATC than the old firm. The new firm could lower the price to as low as
P = ATCO. If the new firm tried to lower their price to stay competitive, their price would be far
below their ATC (ATCN). They would go out of business.
So, as soon as a new firm enters, the old firm could simply lower the price and drive the new
firm out of business. Then we are left with just one firm. And, as we saw earlier, we get less
social welfare with monopoly. No firms will ever enter this industry since they know the old firm
has this big cost advantage. We would be left with a monopoly, which does not maximize social
welfare.
But if the government regulated the price, we could get more social welfare. The question is,
what is the best price to pick?
The two options
1. Make the natural monopoly charge a price equal to their ATC. This is called average total
cost price regulation. We find it in the graph below where the demand line is crossed by the
ATC line (PATC).
2. Make the natural monopoly charge a price equal to their MC. This is called marginal cost
price regulation. We find it in the graph below where the demand line is crossed by the MC line
(PMC).
P,C
PATC
LRATC
PMC
MC
D
D
D
QATC
Q
QMC
At first glance, it looks like marginal cost price regulation is the best choice since we get the
lowest price and the highest quantity. And, we know from earlier that when P = MC, social
welfare is maximized.
But there is a problem. At QMC, the firm’s ATC > P. With marginal cost price regulation, the
firm will lose money and go out of business. In that case, we get no social welfare. We can see in
the graph below that at QMC, the firm’s ATC > P.
P,C
P < ATC
D
PATC
LRATC
PMC
MC
D
D
D
QATC
QMC
Q
The government could pay the firm a subsidy equal to the amount of money that they are losing
to keep them in business (this would mean the firm makes a normal profit, just like if P = ATC).
But a subsidy would require tax dollars. Would it be worth the cost to subsidize the firm to get
the higher social welfare under marginal cost price regulation?
It will be. That is what the next example is about.
P,C
20
18
16
14
12
10
8
6
ATC
4
MC
2
D
2
4
6
8
10 12
14
16
18
20 22
24
26 28
30
Q
To see which policy is the best, average total cost price regulation or marginal cost price
regulation, we need to calculate the social welfare in each case.
The way this example is set up, with both average total cost price regulation or marginal cost
price regulation, all of the social welfare will be consumer surplus. There will be no producer
surplus.
If we have average total cost price regulation, the price will be 8.
If we have average total cost price regulation, the quantity will be 8.
What will the social welfare be (it will all come from consumer surplus)?
Look at the graph below.
P,C
20
18
16
14
12
10
8
6
ATC
4
MC
2
D
2
4
6
8
10 12
14
16
18
20 22
24
26 28
30
Q
The red trianlge above is the social welfare if we have average total cost price regulation. The
social welfare will be
SW = ½*8*8 = 32
How much social welfare will we have if we go with marginal cost price regulation?
If we have marginal cost price regulation the price will be 4.
If we have marginal cost price regulation the quantity will be 12.
BUT, the ATC with marginal cost price regulation will be 7.
See the graph below.
It shows what was mentioned earlier, that the firm will lose money if we go with marginal cost
price regulation.
The thick green line and the two green points whow that P = 4 and that ATC = 7.
So the firm will lose three dollars per unit.
That means their total loss will be 36. To keep them in business, the government would have to
pay the firm a subsidy of 36.
(another graph will illustrate the loss)
P,C
20
18
16
14
12
10
8
6
ATC
4
MC
2
D
2
4
6
8
10 12
14
16
18
20 22
24
26 28
30
In the graph below, the green rectangle shows the amount of the loss when P = 4 and Q = 12
under marginal cost price regulation. The size or area of this rectangle is 36 (3*12).
Q
P,C
20
18
16
14
12
10
8
6
ATC
4
MC
2
D
2
4
6
8
10 12
14
16
18
20 22
24
26 28
Q
30
But how much consumer surplus will we get with marginal cost price regulation? If it is high
enough, even after we subtract out the subsidy, the net social welfare could be more than what
we had under average total cost price regulation (32). In the graph below, the blue rectangle
shows what the social welfare under marginal cost price regulation would be.
P,C
20
18
16
14
12
10
8
6
ATC
4
MC
2
D
2
4
6
8
10 12
14
16
18
20 22
24
26 28
30
Q
The social welfare will be
SW = ½*12*12 = 72
This is more than the 32 we got under average total cost price regulation. BUT, we need to
subtract the 36 from the subsidy to get the net social welfare. That leaves
Net SW = 72 – 36
This is greater than 32, so we get more social welfare with marginal cost price regulation than
with average total cost price regulation, even when we subtract out the cost of the subsidy.
THERE WILL BE A QUESTION LIKE THIS ON THE TEST. IT WILL BE WORTH 25
POINTS. IF YOU DO THAT QUESTION, YOU WILL NOT HAVE TO DO ANY OTHER
ESSAY QUESTIONS (THAT IS, NOT DO A 10 OR 15 POINT QUESTION LIKE THE FIRST
TEST). YOU WILL GET A QUESTION LIKE THIS VERY SOON WITH THE CHAPTER 25
QUESTIONS SO YOU CAN PRACTICE.