Download VII. Monopoly.

Monopoly
What is monopoly?
It is a situation in which there is one seller of
a product for which there are no good
substitutes.
Why do monopolies exist?
1. Economies of scale – costs are lowest
when one firm supplies all the product
(Natural Monopoly)
2. Legal Barriers such as patents (exclusive
right given to inventor/innovator for a
specified period of time) and exclusive
franchises or licenses
3. Control of an essential resource needed
for production
Since the monopolist is the only supplier of
the product, the demand curve for the
industry is the same as the demand curve
for the monopolist’s product.
price
Demand
quantity
$
MC
P*
ATC

ATC*
D
MR
Q
Q*
$
TR
TC
0
Q*
Q
The firm’s profits
are maximized
where MR = MC.
That is where the
slopes of the TR &
TC curves are the
same & where the
gap between the
TR & TC curves is
the largest.
In long run equilibrium, a monopolist produces
the output level where LR MC = MR.
Unlike the perfectly competitive firm,
however, the monopolist can have positive
profits in the LR since high barriers to entry
keep competitors out of the monopolist’s
industry.
Lerner Index
This index measures the amount of control a
firm has over the price of its product or the
extent of its monopoly power.
L = (P – MC) / P
The index is between 0 & 1.
For a perfectly competitive firm, P = MC
& L = 0.
Multiplant Monopoly
Suppose a firm has more than one plant.
How does it determine how much to produce
in each plant?
As usual, the answer involves equating MR
& MC.
Example
Output
MC for
Plant A
MC for
Plant B
MC for
Firm
Price
0
---
---
---
18
1
1
3
16
2
2
7
14
3
4
10
12
4
9
12
10
5
10
15
8
TR
MR
Suppose we have our MC for our two plants, A and B, and the price from the
demand for our product.
Example
Output
MC for
Plant A
MC for
Plant B
MC for
Firm
Price
TR
MR
0
---
---
---
18
0
---
1
1
3
16
16
2
2
7
14
28
3
4
10
12
36
4
9
12
10
40
5
10
15
8
40
We can easily calculate our TR = PQ …
Example
Output
MC for
Plant A
MC for
Plant B
MC for
Firm
Price
TR
MR
0
---
---
---
18
0
---
1
1
3
16
16
16
2
2
7
14
28
12
3
4
10
12
36
8
4
9
12
10
40
4
5
10
15
8
40
0
and our MR.
Example
Output
MC for
Plant A
MC for
Plant B
MC for
Firm
Price
TR
MR
0
---
---
---
18
0
---
1
1
3
1
16
16
16
2
2
7
14
28
12
3
4
10
12
36
8
4
9
12
10
40
4
5
10
15
8
40
0
(from A)
2
(from A)
The firm produces the least expensive units first.
So it makes the 1st and 2nd units in plant A.
So the MC to the firm of making the 1st and 2nd units is the same as the MC of
making the 1st and 2nd units in plant A.
Example
Output
MC for
Plant A
MC for
Plant B
MC for
Firm
Price
TR
MR
0
---
---
---
18
0
---
1
1
3
1
16
16
16
2
2
7
14
28
12
3
4
10
12
36
8
4
9
12
10
40
4
5
10
15
8
40
0
It makes the 3rd unit in plant B,
(from A)
2
(from A)
3
(from B)
Example
Output
MC for
Plant A
MC for
Plant B
MC for
Firm
Price
TR
MR
0
---
---
---
18
0
---
1
1
3
1
16
16
16
2
2
7
14
28
12
3
4
10
12
36
8
4
9
12
10
40
4
5
10
15
8
40
0
the 4th unit in plant A,
(from A)
2
(from A)
3
(from B)
4
(from A)
Example
Output
MC for
Plant A
MC for
Plant B
MC for
Firm
Price
TR
MR
0
---
---
---
18
0
---
1
1
3
1
16
16
16
2
2
7
14
28
12
3
4
10
12
36
8
4
9
12
10
40
4
5
10
15
8
40
0
and the 5th unit in plant B.
(from A)
2
(from A)
3
(from B)
4
(from A)
7
(from B)
Example
Output
MC for
Plant A
MC for
Plant B
MC for
Firm
Price
TR
MR
0
---
---
---
18
0
---
1
1
3
1
16
16
16
2
2
7
14
28
12
3
4
10
12
36
8
4
9
12
10
40
4
5
10
15
8
40
0
(from A)
2
(from A)
3
(from B)
4
(from A)
7
(from B)
So we can see that the MC for the firm as a whole is built from the MC values
from the two plants.
Example
Output
MC for
Plant A
MC for
Plant B
MC for
Firm
Price
TR
MR
0
---
---
---
18
0
---
1
1
3
1
16
16
16
2
2
7
2
14
28
12
3
4
10
3
12
36
8
4
9
12
4
10
40
4
5
10
15
7
8
40
0
Then the firm produces the output that equates the firm’s MC to MR.
So the firm produces 4 units.
(MR and MC happen to be 4 as well. MR and MC don’t have to be the same as
the output level. MR and MC just have to be equal to each other.)
A supply curve
indicates the price
at which the firm
would be willing to
provide various
quantities.
However, the
monopolist
determines the
profit- maximizing
output from
MR=MC and then
sets the price from
the demand curve.
So there is no
independent supply
curve.
Note: The monopolist does not
have a supply curve.
P
Pm
MC
MR
Qm
Qc
D
Q
Suppose we want to compare the perfectly
competitive industry and the monopolistic industry.
Recall that in perfect competition, the firm’s supply
curve is the MC curve above the minimum of the AVC
curve. The supply curve for the perfectly competitive
industry is the horizontal sum of the individual firms’
supply curves.
So, if we want to compare the monopolistic industry
and the perfectly competitive industry, the monopolist’s
MC curve would be comparable to the perfectly
competitive industry’s supply curve.
How do output and price compare in the
monopolistic industry versus the perfectly
competitive industry?
Recall that output
and price in the
perfectly competitive
industry are
determined by the
intersection of the
supply and demand
curves.
P
Pm
MC or S
Pc
So in perfect
competition, output
and price are Qc and
Pc respectively.
In monopoly, as we
stated earlier, output
and price are Qm
and Pm .
MRmonopolist
Qm
Qc
D
Q
How do output and price compare in the
monopolistic industry versus the perfectly
competitive industry?
Note that
Q m < Qc
P
and
Pm > Pc .
That is, the
monopolistic
industry produces
a lower level of
output and
charges a higher
price than the
perfectly
competitive
industry does.
Pm
MC or S
Pc
MRmonopolist
Qm
Qc
D
Q
Welfare loss of monopoly
compared to perfect competition
Recall that
consumer surplus
is the area above
the price & below
the demand curve.
Producer surplus
is the area below
the price & above
the supply curve
or, in the case of
the monopolist,
above the MC
curve.
P
Pm
MC or S
Pc
MRmonopolist
Qm
Qc
D
Q
In the perfectly competitive case, quantity & price
are determined by the intersection of the supply &
demand curves.
Then
consumer
surplus is the
purple triangle.
Producer
surplus the
green triangle.
P
Pm
MC or S
Pc
MRmonopolist
Qm
Qc
D
Q
In monopoly, the quantity is where MR = MC & the
price comes from the D curve above that quantity.
P
Consumer
surplus is the
pinkish triangle. Pm
Producer
Pc
surplus is the
yellow region.
MC or S
MRmonopolist
Qm
Qc
D
Q
The difference in the combined consumer &
producer surpluses is the light purple area.
This is the loss
of welfare
when
monopoly is
compared to
perfect
competition.
P
Pm
MC or S
Pc
MRmonopolist
Qm
Qc
D
Q
Natural Monopoly
a situation in which ATC declines
continually with increased output.
So a single firm would be the lowest cost
producer of the output demanded.
ATC doesn’t turn upward until a very high
output level, beyond the amounts that
consumers will buy.
$
ATC
quantity
Remember: the MC curve is below the ATC
curve when ATC is sloping downward.
$
MC
ATC
quantity
Draw the demand and MR curves.
$
D
MC
MR
ATC
quantity
Natural Monopoly:
operating freely
$
D
P*
MR
MC
ATC
Q*
quantity
Regulation
marginal cost pricing (P = MC)
average cost pricing (P = ATC)
Natural Monopoly:
marginal cost pricing regulation
$
D
MC
Pm
MC pricing uses the price
where MC intersects D.
But at that point, P < ATC .
Firm has a loss!
So this won’t work.
MR
ATC
Qm quantity
Natural Monopoly:
Average Cost Pricing Regulation
$
PR
If the government uses average cost pricing to regulate a monopolist,
the price PR is set where the demand curve intersects the ATC curve.
Since P = ATC, the firm will have zero economic profits.
So this can work.
In this situation, the firm sees
the demand curve for its
product as the orange line.
The MR curve would be the
ATC
MC
bright blue line.
The firm would equate MR to
MC and produce QR.
D
MR
QR
Q
Example
A monopolist faces the following situation.
Demand: P = 300 – 3 Q
TC = Q3 – 21 Q2 + 333 Q + 180
(a) Determine the profit-maximizing output,
price, TR, TC & profit if the monopolist
operates without regulation.
(b) Determine the output, price, TR, TC & profit
if the monopolist is regulated using average
cost pricing.
(a) monopolist operating without regulation
Demand: P = 300 – 3 Q
TC = Q3 – 21 Q2 + 333 Q + 180
To maximize profits, the firm will set MR = MC.
TR = PQ = 300 Q – 3 Q2
MR = dTR/dQ = 300 – 6Q
MC = dTC/dQ = 3Q2 – 42 Q + 333
Equate MR = 300 – 6Q to MC = 3Q2 – 42 Q + 333
300 – 6Q = 3Q2 – 42 Q + 333
0 = 3Q2 – 36 Q + 33
Dividing through by 3, we find
0 = Q2 – 12 Q + 11
0 = (Q – 1) (Q – 11)
So Q = 1 or Q = 11
It can be shown using the second derivative of
the total profit function that profit is maximized
at Q = 11 and minimized at Q = 1.
So at the maximum, where Q = 11:
P = 300 – 3 Q = 300 – 3(11) = 300 – 33 = 267
TR = PQ = (267)(11) = 2937
TC = Q3 – 21 Q2 + 333 Q + 180
= (11)3 – 21 (11)2 + 333(11) + 180
= 2633
Profit = TR – TC = 2937 – 2633 = 304
(b) Monopolist regulated by average cost pricing
Demand: P = 300 – 3 Q
TC = Q3 – 21 Q2 + 333 Q + 180
ATC = TC/Q = Q2 – 21 Q + 333 + (180/Q)
Plotting points & graphing ATC & D, you see
that they intersect when Q = 15.
At that output,
P = 300 – 3 Q = 300 – 3(15) = 255, and
ATC = Q2 – 21 Q + 333 + (180/Q)
= (15)2 – 21 (15) + 333 + (180/15) = 255
So the regulator sets the price at 255 & the firm
produces 15 units of output.
With P = 255 & Q = 15:
TR = PQ = (255)(15) = 3825
TC = Q3 – 21 Q2 + 333 Q + 180
= (15)3 – 21(15)2 + 333 (15) + 180 = 3825
[or TC = ATC(Q) = 255(15) = 3825]
Economic profit = TR – TC = 0
& firm makes just a normal accounting profit.