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Chapter 5 & 6 .2.1
Main Monopoly
REVENUE
• Revenue curves when price varies with
output (downward-sloping demand curve)
Revenues for a firm facing a downward sloping
demand curve
Q (units)
P (£)
TR (£)
AR (£)
1
8
8
8
2
7
14
7
3
6
18
6
4
5
20
5
5
4
20
4
6
3
18
3
7
2
14
2
REVENUE
• Revenue curves when price varies with
output (downward-sloping demand curve)
– average revenue (AR)
TR P.Q
AR 

P
Q
Q
AR and MR curves for a firm facing a downward-sloping D curve
Q P =AR
(units) (£)
8
1
7
2
6
3
5
4
4
5
3
6
2
7
8
AR, MR (£)
6
4
2
TR MR
(£) (£)
8
6
14
4
18
2
20
0
20
-2
18
-4
14
AR
0
1
2
3
4
5
6
7
-2
-4
MR
Quantity
Why is the MR curve below the Demand
Curve
dTR
MR 
but TR  P.Q
dQ
d [ P.Q]
MR 
dQ
To differentiate P.Q we use the
product rule. Let u=P and v=Q
d [ P.Q]
dQ
dP
P
Q
dQ
dQ
dQ
d [ P.Q]
dP
 PQ
dQ
dQ
d [u.v]
dv
du
u
v
dQ
dQ
dQ
Why is the MR curve below the Demand
Curve?
dTR d [ P.Q ]
dP
MR 

 P Q
dQ
dQ
dQ
Why is the MR curve below the Demand
Curve?
dP
MR  P  Q
dQ
•MR = AR + something negative
AR and MR curves for a firm facing a downward-sloping D curve
Q P =AR
(units) (£)
8
1
7
2
6
3
5
4
4
5
3
6
2
7
8
AR, MR (£)
6
4
2
TR MR
(£) (£)
8
6
14
4
18
2
20
0
20
-2
18
-4
14
AR
0
1
2
3
4
5
6
7
-2
-4
MR
Quantity
TR curve for a firm facing a downward-sloping D curve
20
Now to sell more have to lower price
16
So gain from additional sales has to
be weighed against lower price on
all goods.
TR (£)
12
8
At some point Revenue will be
maximized
TR
4
0
0
1
2
3
4
Quantity
5
6
7
TR curve for a firm facing a downward-sloping D curve
20
16
Quantity P = AR
(units)
(£)
TR (£)
12
1
2
3
4
5
6
7
8
4
TR
(£)
8
7
6
5
4
3
2
8
14
18
20
20
18
14
5
6
0
0
1
2
3
4
Quantity
7
TR curve for a firm facing a downward-sloping D curve
20
16
Quantity P = AR
(units)
(£)
TR (£)
12
1
2
3
4
5
6
7
8
4
TR
TR
(£)
8
7
6
5
4
3
2
8
14
18
20
20
18
14
5
6
0
0
1
2
3
4
Quantity
7
TR curve for a firm facing a downward-sloping D curve
For a maximum, derivative of TR function
must be equal to Marginal costs
dTR
But
 MR
dQ
MR  MC
TR curve for a firm facing a downward-sloping D curve
20
16
TR
TR (£)
12
8
4
0
0
1
2
3
4
Quantity
5
6
MR
7
MONOPOLY
• Essential Characteristics of the monopolist's
demand curve
– downward sloping
– MR below AR
Profit maximising under monopoly
£
AR
MR
O
Q
Profit maximising under monopoly
£
MC
AC
AR
MR
O
Q
Profit maximising under monopoly
£
MC
MR=MC rule
still applies
Determines
Qm
MR
O
Qm
Q
Profit maximising under monopoly
£
AR
MC
Given
MR=MC, we
then find Price
at Qm
a
AR
MR
O
Qm
Q
Profit maximising under monopoly
£
AR
AC
..and
profits?
MC
AC
a
b
AR
MR
O
Qm
Q
MONOPOLY
• Defining monopoly
• Barriers to entry
• Natural monopoly
MONOPOLY
• Defining monopoly
• Barriers to entry
– economies of scale
– product differentiation and brand loyalty
– lower costs for an established firm
– ownership or control over key factors
– ownership or control over outlets
– legal restrictions
– mergers and takeovers
– aggressive tactics
– intimidation
MONOPOLY
• Disadvantages of monopoly
– high prices / low output
Equilibrium of industry under perfect competition and monopoly:
with the same MC curve
£
MC
P1
AR = D
MR
O
Q1
Q
Equilibrium of industry under perfect competition and monopoly:
with the same MC curve
£
MC
P1
P2
AR = D
MR
O
Q1
Q2
Q
Equilibrium of industry under perfect competition and monopoly:
with the same MC curve
£
MC ( = supply under
perfect competition)
P1
P2
AR = D
MR
O
Q1
Q2
Q
MONOPOLY
• Disadvantages of monopoly
– high prices / low output: short run and long run
MONOPOLY
Is monopoly ever an advantage?
Yes, if economies of scale are significant.
Also, monopoly profits may be necessary to
“fuel” innovation (think of medical industry)
Natural Monopoly
£
LRAC
MC
O
Q
Industry Demand Curve D
£
If two firms in the
industry (A Duopoly)
the demand curve for
each is DD
(half the market)
DD
O
D
Q
Natural Monopoly
£
Since LRAC is always
above AR no production
occurs (in the long run)
NOTE: Decreasing LRAC,
constant MC (big initial
investment, but low “per
unit” costs)
DD
LRAC
MC
MR
O
Q0
Q
Natural Monopoly
£
Dm
With one firm, however,
DD
LRAC
MC
O
Qm
Q
Natural Monopoly
£
Dm
With one firm, however,
equilibrium occurs at Qm
Pm
LRAC
MC
MR
O
Qm
Q
Natural Monopoly
£
Dm
With one firm, however,
equilibrium occurs at Qm
Pm
LRAC
MC
MR
O
Qm
Q
Natural Monopoly
• Here with just two firms, no production at all
• But with monopoly production takes place
that would not otherwise happen.
• There may be supernormal profits, but scale
of production allows lower cost and a
(profitable) market price agents are willing
to pay.