Introductory Microeconomics
(ES10001)
Topic 6: Imperfect Competition
1
1. Introduction

PC & Monopoly are useful benchmarks.

But, in more than half of the 800 major UK
manufacturing product categories, 70% of market is
shared by 5 largest firms in the market.

Real world markets are imperfectly competitive

Imperfectly competitive (IC) firms cannot sell as
much as want at going market price; they face a
downward sloping demand curve.
2
1. Introduction

Two models of imperfect competition
Monopolistic Competition
Oligopoly

And in terms of Oligopoly
Non-Collusive
Collusive
3
2. Monopolistic Competition

Theory originally developed by Chamberlain (USA)
and Robinson (UK) in early 1930s

Many sellers producing similar, but not identical,
products that are close substitutes for each other

Each firm has only a limited ability to affect the
market price
4
2. Monopolistic Competition

Assumptions:

Large number of small firms; firms assume own
behaviour has no influence on rivals actions;

Similar, but not identical, products;

Free entry and exit into industry
5
2. Monopolistic Competition

Implication

Each firm can, to some extent, influence its market
share by changing its price relative to its competitors

Demand curve is downward sloping because
different firms’ products are only limited substitutes
for each other

Advertising; product differentiation
6
2. Monopolistic Competition

Short-run equilibrium of typical monopolistically
competitive firm

Profit-maximising monopolist in its own brand

Thus MR = MC and (we assume) profit > 0
7
Figure 1: Monopolosit Competition (SR)
p
π>0
SMC
p0
SAC
Profit
LAC0
D = AR
MR
0
Q0
Q
8
2. Monopolistic Competition

Existence of supernormal profit induces other firms
to enter industry with their own brands

This shifts down/left demand curve facing existing
monopolistically competitive firms

Moreover, demand curve becomes more elastic since
consumers now have a greater variety of choice

Process continues until no more firms enter industry
(i.e. all firms are earning normal profit)
9
Figure 2: Impact on AR of entry of rival brands
p
AR0
AR1
0
Q
10
Figure 3: Monopolist LR Equilibrium
p
π=0
LMC
LAC
p0 = LAC0
MR
0
Q0
D = AR
Q
11
2. Monopolistic Competition

Long-run tangency equilibrium where p = LAC

Monopolistically competitive firms are neither
electively nor productively efficient

‘... too many firms each producing too little output.’
(Chamberlain)

But …
‘... excess capacity is the cost of differentness.’
12
3. Oligopoly

‘Competition among the few’

Few producers, each of whom recognises that its
own price depends on both its own output and the
output of its rivals

Thus, firms are of a size and number that each must
consider how its own actions affect the decisions of
its relatively few competitors.

For example, firm must consider likely response of
rivals before embarking on a price cutting strategy
13
3. Oligopoly

Collusion or competition?

Key element of all oligopolistic situations

Collusion; agreement between existing firms to
avoid competition with one another

Can be explicit or implicit
14
3. Oligopoly

For example, existing firms might collude to
maximise joint profits by behaving as if they were a
multi-plant monopolist

i.e. restricting q to monopolist level, say q0, and then
negotiating over the division of q and monopoly
profits

Note, might not agree to divide up q equally;
sensible for more efficient members of the cartel to
produce q
15
Figure 4: Collusion or Competition
p
p0
E0
p1
MC
MR
0
q0
D = AR
q1
q
16
3. Oligopoly

But, since cartel p > MC, each firm has an incentive
to renege on the collusive agreement

... temptation to reach the ‘first best’ renders the
‘second best’ unsustainable and drives firms to
‘third best’
First-Best:
Second-Best:
Third-Best:

I renege, you collude
Neither renege; we both collude
We both renege
Cartels are inherently fragile!
17
Figure 4: Collusion or Competition
p
Cartel price is above cartel
member’s marginal cost,
thus incentive to renege
(i.e. increase q)
p0
Normal profit
equilibrium
p1
MC
MR
0
q0
D = AR
q1
q
18
3. Oligopoly

Collusion is easiest when formal agreements
between firms are legally permitted (e.g. OPEC).

More common in 19th century, but increasingly
outlawed

Collusion is more difficult the more firms there are
in the market, the less the product is standardised,
and the more demand and cost conditions are
changing in the absence of collusion
19
3. Oligopoly

In absence of collusion, each firm’s demand curve
depends upon how competitors react, and firms have
to make assumptions about this

A simple model of this was developed by Sweezy
(1945) to explain that apparent fact that prices once
set as a mark-up on average costs, tend not too
change

‘Kinked Demand Curve’ model
20
3. Oligopoly

Assume firm is at E0 selling q0 output at a unit price
of p0

Firm believes that if it raises price, its rivals will not
raise their price (i.e. DA), but that if it lowers price,
then its rivals will follow him (i.e. DB)

Thus demand curve is kinked at E0 being flatter for p
> p0 and steeper for p < p0
21
Figure 5a: Kinked Demand Curve Model
p
p0
E0
DA
DB
0
q0
q
22
3. Oligopoly

Both the ‘no-follow’ demand curve (DA) and the
‘follow’ demand curve (DB) will have an associated
MR curve (MRA, MRB)

Thus MR is discontinuous (i.e. vertical) at q0 since an
increase in q beyond q0 will lead to a discontinuous
fall in total revenue
23
Figure 5b: Kinked Demand Curve Model
p
p0
E0
DA
DB
0
q
q0
MRB
MRA
24
Figure 5c: Kinked Demand Curve Model
p
p0
E0
D
0
q
q0
MR
25
3. Oligopoly

Thus, fluctuations in marginal cost within the
discontinuous part of the MR curve (i.e. within A-B)
do not lead to a change in the firms profitmaximising level of output

Sweezy used the model to model the inflexibility of
US agricultural prices in the face of cost changes
26
Figure 5a: Kinked Demand Curve Model
p
p0
LMC
E0
A
B
D
0
q
q0
MR
27
3. Oligopoly

But two key weaknesses:

Empirical
Further evidence suggested that agriculture prices
did not behave asymmetrically

Theoretical
Model does not explain how we got to the initial
equilibrium, or where we go if LMC moves outside
of the discontinuity
28
3. Oligopoly

Cournot (1833)

Firms compete over quantities with ‘conjectural
variation’ that other firm(s) will hold their output
constant

Cournot originally envisaged two firms producing
identical spring water at zero cost
29
3. Oligopoly

Two firms (a, b) costlessly produce identical spring
water

Assume normal (inverse) demand curve for spring
water is:
qd = 100 – 5p <=> pd= 20 – 0.2q

Assume that firm a believes that firm b will produce
zero output (i.e. Ea{qb}= 0); firm a’s optimal q is
that which maximises firm a’s total revenue vis.
*
qa1
= 50
30
Figure 6a: Cournot Competition
p
Firm a’s optimal output if Ea{qb}= 0
20
d
qa1
= q d = 100 - 5p
Þ
*
qa1
= 50
Ea1
10
D = AR
0
50
100
q
MR
31
3. Oligopoly

However, if firm a were to produce 50 units, then
firm b would presume that it (i.e. firm b) faces a
(residual) demand curve of:
(
)
*
qb1d = q d - qa1
= 100 - 5p - 50 = 50 - 5p

i.e. a residual demand given by the market demand
for the good less firm a’s output

And firm b would make its optimal choice of output
accordingly
32
Figure 6b: Cournot Competition
p
Firm a’s supply
Firm b’s (residual) demand
20
*
qb1d = q d - qa1
Þ
Ea1
10
(
)
qb1d = 100 - 5p - 50
Þ
qb1d = 50 - 5 p
D´ = AR´
0
50
100
MR
MR´
q
33
Figure 6c: Cournot Competition
p
Firm b’s residual demand
10
d
qb2
= 50 - 5p
Þ
*
qb2
= 25
Eb2
5
D = AR
0
25
50
q
MR
34
3. Oligopoly

Thus, if qa = 50, then firm b would maximise its
profit (i.e. revenue) by setting qb = 25

But this would imply that firm a would want to
change its initial level of output; i.e. qa1 = 50 was
optimal under the assumption that qb = 0

But now that qb = 25, firm a will want to revise its
choice of q accordingly
35
3. Oligopoly

Thus, firm a will choose the level of output that
maximises total revenue given qb = 25

Firm a’s residual demand curve is thus:
(
)
d
*
qa3
= q d - qb2
= 100 - 5p - 25 = 75 - 5p

Such that
*
qa3
= 37.5
36
Figure 6d: Cournot Competition
p Firm a’s supply
Firm a’s (residual) demand
20
15
d
*
qa3
= q d - qb2
Þ
Eb2
d
qa3
= (100 - 5p ) - 25
Þ
d
qa3
= 75 - 5p
MR´
0
25
D´ = AR´
100
q
37
Figure 6e: Cournot Competition
p
Firm a’s residual demand
15
d
*
qa3
= q d - qb2
= (100 - 5 p ) - 25
Þ
Ea3
7.5
d
qa3
= 75 - 5p
Þ
*
qa3
= 37.5
D = AR
0
37.5
75
q
MR
38
3. Oligopoly

This process will continue until neither firm ‘regrets’
its optimal choice of output

i.e. until its ‘conjectural variation’ regarding the
other firm’s response is validated

The Cournot equilibrium is thus where:
qa* = 33.3 = qb*
39
Figure 6d: Cournot Competition
p
Cournot Equilibrium
20
Ea
Eb
D = AR
0
33.3
33.3
100
q
MR MR´
40
3. Oligopoly

Cournot market shares
Round
Firm a
Firm b
1
50
0
2
50
25
3
37.5
25
4
n
37.5 33.33
31.25 33.33
41
3. Oligopoly

It can be shown that total (i.e. market) equilibrium
output under Cournot competition is given by:
æ n ö c
q =ç
q
÷
è n + 1ø
n

where qc is the perfectly competitive level of output
(i.e. where p = MC)

N.B. Usually termed ‘Nash-Cournot’ equilibrium,
hence superscript ‘n’
42
3. Oligopoly

Solution method without calculus:

Firm a’s residual demand curve:
qa* = q d - qb* = (100 - 5p ) - qb*
Þ
*
æ
100 - qb ö 1 *
*
*
pa º ARa = ç
- 5 qa
÷
5 ø
è
43
3. Oligopoly

Thus:
*
æ
ö 1 *
100
q
*
*
b
pa º ARa = ç
- 5 qa
÷
5 ø
è
Þ
*
æ
ö 2 *
100
q
*
b
MRa = ç
- 5 qa
÷
5 ø
è
44
3. Oligopoly

Setting MR = 0 implies:
*
æ
ö 2 *
100
q
*
2
MRa = ç
- 5 qa = 0
÷
5 ø
è
Þ
*
2
q
q = 50 2
*
a
45
3. Oligopoly

And similarly for Firm b, thus, two equations and
two unknowns:
*
qb
*
qa = 50 2
*
q
qb* = 50 - a
2

Solving …
46
3. Oligopoly
*
q
qa* = 50 - b = 50 2
*
*
æ
ö
q
q
a
a
1
50
=
25
+
2ç
2 ÷ø
4
è
Þ
4qa* = 100 + qa*
Þ
3qa* = 100
Þ
qan = 33.33 = qbn
47
3. Oligopoly

Generally, assume:
q d = a - bp
Þ
pd = a b -
1
b
q = a - bq

where a = a b , b =

And assume MCa = c = MCb
1
b
-q
48
3. Oligopoly

Thus:
(
)
qa* = a - qb* - bp
Þ
*
æ
ö
a
q
*
*
b
pa º ARa = ç
÷
è b ø
1
b
q
*
a
Þ
*
æ
ö
a
q
*
*
b
2
MRa = ç
- b qa
÷
è b ø
49
3. Oligopoly

Generally:
*
æ
ö
a
q
*
b
2 q * = c = MC
MRa = ç
b a
÷
è b ø
Þ
(
1
q = a - bc - qb*
2
*
a
)
50
3. Oligopoly

Thus:
(
) (
1
1
*
q = a - bc - qb = a b - bc - qb*
2
2
Þ
*
a
)
1
1 éæ a - c ö
*
*ù
q = éë(a - c ) b - qb ùû = êç
- qb ú
÷
2
2 ëè b ø
û
Þ
*
a
(
)
1
q = q - qb* , where q = (a - c ) b
2
*
a
51
3. Oligopoly

Thus:
(
)
(
1
1
*
*
*
q = q - qb , qb = q - qa
2
2
Þ
*
a
(
1
2q = q - q = q - q - qa*
2
Þ
*
a
*
b
(
4qa* = 2q - q - qa*
)
)
)
52
3. Oligopoly

Thus:
(
4qa* = 2q - q - qa*
)
Þ
3qa* = q
Þ
q =
n
a
q
3
=q
n
b
53
3. Oligopoly

Thus:
1æ a - cö
q = = ç
3 3 è b ÷ø
n
i
q
Þ
a - cö
æ
1
a - bc
n
b
qi = ç 1 ÷ =
3è b ø
3

since a = a b , b =
1
b
-q
54
3. Oligopoly

Recall:
q d = 100 - 5 p, c = 0
Þ
a - bc 100 - 5×0
q =
=
3
3
Þ
n
i
qin = 33.33
55
3. Oligopoly

Monopoly
n = 1 Þ qn = (1/2)qc

Duopoly
n = 2 Þ qn = (2/3)qc

Perfect Competition
n = ¥ Þ qn = q c
56
3. Oligopoly

Cournot originally envisaged his model in term of
sequential decision making on the part of firms

But it would irrational for each firm to persist with
the conjectural variation that its rival will hold
output constant when they only do so in equilibrium

Moreover, the model implies the existence of a
future, in which case it can be shown that profitable
collusion is sustainable
57
3. Oligopoly

Economists have re-interpreted Cournot’s model in
terms of a one-shot game

i.e. only one amount of output actually put onto
market vis. Cournot equilibrium level of output qn

But, it is assumed that each firm goes through a
rational sequential decision making process before
implementing its output choice
58
3. Oligopoly

The Cournot equilibrium may be re-interpreted in
this sense as a Nash Equilibrium

That is, an equilibrium in which each party is
maximising his utility given the behaviour of all the
other parties

I am doing the best I can do, given what you are
doing; and vice versa
59
3. Oligopoly

Stackelberg competition

Variation of Cournot in which firm a announces its
output and, once that announcement is made, the
output cannot be changed.

i.e. one-shot game or repeated game in which firm a
produces the same level of output in each period.
60
3. Oligopoly

Assume:
Firm 1 - market ‘leader’
Firm 2 - market ‘follower’

N.B. firm 1 has to be able to make a credible,
binding commitment to a particular output level
61
Figure 7: Stackelberg Competition
p
q d = 100 - 5 p
Þ
20
q1s = 50
q2s = 25
E1
E2
Es
5
0
D´ = AR´
50
25
MR
75
MR´
100
q
62
3. Oligopoly

Bertrand Competition

Both Cournot and Stackelberg assume that firms
chose outputs with prices determined by the inverse
demand functions.

But in many oligopolistic markets firms appear to set
prices and then sell whatever the market demands at
those prices
63
3. Oligopoly

In perfect competition and monopoly, it makes no
difference whether we carry out analysis in terms of
prices or quantities

That is, price determines quantity and quantity
determines price

But in oligopoly the distinction is crucial
64
3. Oligopoly

Bertrand presented an alternative to the Cournot
model in his review of Cournot’s book.

He asked the question, what would be the outcome if
the two firms chose prices:
(a) simultaneously
(b) independently

And then sold all the output that was demanded at
these prices via the inverse demand functions
65
3. Oligopoly

Conclusion

Completely different result emerges

Equilibrium which replicates perfectly
competitive (i.e. allocatively efficient)
equilibrium in which p = MC
66
3. Oligopoly

Firms compete with each other by marginally
undercutting the other’s price (assuming
homogenous good, costs etc.) and thus taking the
whole market

Process continues until the only equilibrium is one
where each firm sets price equal to marginal cost
67
3. Oligopoly

Nash equilibrium in Bertrand is p1 = MC = p2

Rationalisation for the equilibrium is on the same
lines as in Cournot model vis. no other pair of prices
has the property of mutual consistency.

Bertrand intended this to be a reductio ad absurdum
and to demonstrate the weakness of Cournot’s
approach
68
Figure 8: Bertrand Competition
p
Monopoly Equilibrium
Em
pm
Bertrand Equilibrium
Eb
pb
MC = AC
D = AR
0
qm
qb
q
MR
69
3. Oligopoly

Bertrand model yields a striking prediction
from a quite reasonable model

If outputs are homogenous, an increase in the
number of firms in the market from one to
two leads from the monopoly equilibrium
directly to the perfectly competitive
equilibrium!
70
4. Game Theory

Game; situation in which intelligent decisions are
necessarily interdependent

The players in the game attempt to maximise their
own payoffs via a strategy

Strategy; game plan describing how the player will
act (or move) in every conceivable situation.

Equilibrium Concept - Nash
71
4. Game Theory

Nash equilibrium occurs when each player
chooses his best strategy, given the strategies
of the other players.

Consider …

Prisoners’ Dilemma
72
4. Game Theory

Prisoner’s Dilemma
Player 2
Confess
Deny
Confess
-8, -8
0, -10
Deny
-10, 0
-1, -1
Player 1
73
4. Game Theory

Prisoner’s Dilemma
Player 2
Confess
Deny
Confess
-8, -8
0, -10
Deny
-10, 0
-1, -1
Player 1
74
4. Game Theory

Prisoner’s Dilemma
Player 2
Confess
Deny
Confess
-8, -8
0, -10
Deny
-10, 0
-1, -1
Player 1
75
4. Game Theory

Prisoner’s Dilemma
Player 2
Confess
Deny
Confess
-8, -8
0, -10
Deny
-10, 0
-1, -1
Player 1
76
4. Game Theory

Prisoner’s Dilemma
Player 2
Confess
Deny
Confess
-8, -8
0, -10
Deny
-10, 0
-1, -1
Player 1
77
4. Game Theory

Prisoner’s Dilemma
Player 2
Confess
Deny
Confess
-8, -8
0, -10
Deny
-10, 0
-1, -1
Player 1
78
4. Game Theory

Prisoner’s Dilemma
Player 2
Confess
Deny
Confess
-8, -8
0, -10
Deny
-10, 0
-1, -1
Player 1
79
4. Game Theory

Prisoner’s Dilemma
Player 2
Confess
Deny
Confess
-8, -8
0, -10
Deny
-10, 0
-1, -1
Player 1
80
4. Game Theory

Prisoner’s Dilemma
Player 2
Confess
Deny
Confess
-8, -8
0, -10
Deny
-10, 0
-1, -1
Player 1
81
4. Game Theory

Prisoner’s Dilemma
Player 2
Confess
Deny
Confess
-8, -8
0, -10
Deny
-10, 0
-1, -1
Player 1
82
4. Game Theory

Prisoner’s Dilemma
Player 2
Confess
Deny
Confess
-8, -8
0, -10
Deny
-10, 0
-1, -1
Player 1
83
4. Game Theory

Prisoner’s Dilemma
Player 2
Confess
Deny
Confess
-8, -8
0, -10
Deny
-10, 0
-1, -1
Player 1
84
4. Game Theory

Prisoner’s Dilemma
Player 2
Confess
Deny
Confess
-8, -8
0, -10
Deny
-10, 0
-1, -1
Player 1
85
4. Game Theory

Prisoner’s Dilemma
Player 2
Confess
Deny
Confess
-8, -8
0, -10
Deny
-10, 0
-1, -1
Player 1
86
4. Game Theory

Prisoner’s Dilemma
Player 2
Confess
Deny
Confess
-8, -8
0, -10
Deny
-10, 0
-1, -1
Player 1
87
4. Game Theory

Prisoner’s Dilemma
Player 2
Confess
Deny
Confess
-8, -8
0, -10
Deny
-10, 0
-1, -1
Player 1
88
4. Game Theory

Prisoner’s Dilemma
Player 2
Confess
Deny
Confess
-8, -8
0, -10
Deny
-10, 0
-1, -1
Player 1
89
4. Game Theory

Prisoner’s Dilemma
Player 2
Confess
Deny
Confess
-8, -8
0, -10
Deny
-10, 0
-1, -1
Player 1
90
4. Game Theory

Prisoner’s Dilemma
Player 2
Confess
Deny
Confess
-8, -8
0, -10
Deny
-10, 0
-1, -1
Player 1
91
4. Game Theory

Nash Equilibrium ; Confess, Confess

Indeed, to confess is each player’s ‘dominant
strategy vis. optimal strategy that is independent of
the strategy of the other player(s)

Recall, ‘collusion versus competition’
92
4. Game Theory

Collusion versus Competition
Firm 2
Renege
Collude
Renege
-8, -8
0, -10
Collude
-10, 0
-1, -1
Firm 1
93
4. Game Theory

Collusion versus Competition
Firm 2
Renege
Collude
Renege
-8, -8
0, -10
Collude
-10, 0
-1, -1
Firm 1
94
4. Game Theory

Collusion versus Competition
Firm 2
Renege
Collude
Renege
-8, -8
0, -10
Collude
-10, 0
-1, -1
Firm 1
95
4. Game Theory

Collusion versus Competition
Firm 2
Renege
Collude
Renege
-8, -8
0, -10
Collude
-10, 0
-1, -1
Firm 1
96
4. Game Theory

Collusion versus Competition
Firm 2
Renege
Collude
Renege
-8, -8
0, -10
Collude
-10, 0
-1, -1
Firm 1
97
3. Oligopoly

First-best (i.e. dominant strategy) would be to
renege given that the other firm colludes

Second-best would to both collude (i.e. a voluntary
agreement to maintain the cartel output – but
restrictive practices are usually illegal and so
agreements are usually tacit)

Third-best is to both renege and compete
98
3. Oligopoly

Again …

…

Temptation to reach the first-best renders the secondbest unsustainable and so forces players to the thirdbest
99