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ECON191 (Spring 2011)
4 & 6.5.2011 (Tutorial 10)
Chapter 12 Monopolistic Competition and Oligopoly
Monopolistic competition

Market in which firms can enter freely, each producing its own brand or version of a
differentiated product

Key characteristics:
(1) Firms compete by selling differentiated products that are highly substitutable. The cross
elasticities of demand are large
(2) Free entry and exit

The amount of monopoly power depends on the degree of differentiation
Equilibrium in the SR and the LR
Short-run

Demand is downward sloping (differentiated products) and is relatively elastic (close
substitutes are available)

Profits are maximized when MR = MC. P > MR = MC as the firm has monopoly power
to a certain extent

This firm is making economic profits






Long-run
Profits will attract new firms to the industry (no barriers to entry)
The existing firm’s demand will decrease to DLR
Firm’s output and price will fall
Industry output will rise
No economic profit (P = AC)
P > MC (some monopoly power)
1
Monopolistic competition and economic efficiency

The monopoly power yields a higher price than perfect competition and is not efficient
which comes from the following two sources:
(1) P > MC
 If price was lowered to the point where MC = D, consumer surplus would increase by
the yellow triangle (Deadweight loss)
(2) Excess capacity
 With no economic profits in the long run, the firm is still not producing at minimum AC
and excess capacity exists.
 Firm faces downward sloping demand so zero profit point is to the left of minimum
average cost
 Excess capacity is inefficient because average cost would be lower with fewer firms

Inefficiencies would make consumers worse off, should monopolistic competition be
regulated? NO
(1) Market power relatively small and deadweight loss is small
(2) Inefficiency is balanced by the benefit of increased product diversity which may easily
outweigh deadweight loss
2
Oligopoly

Oligopoly: market or industry with two or a few firms. The simplest case is Duopoly.




Characteristics:
Small number of firms
Product differentiation may or may not exist
Barriers to entry (Scale economies, Patents, Technology, Name recognition, Strategic
action)
The Cournot model

Oligopoly model in which firms produce a homogeneous good, each firm treats the
output of its competitors as fixed, and all firms decide simultaneously how much to
produce

Firm 1’s profit-maximizing output depends on how
much it thinks that Firm 2 will produce.

If it thinks Firm 2 output = 0, Firm 1’s demand curve is
D1(0), which is the market demand curve. The
corresponding MR curve is MR1(0)
Firm 1 produces 50 units where MC1 = MR1




If Firm 1 thinks that Firm 2 will produce 50 units, its
demand curve becomes D1(50) and profit maximizing
output = 25
If Firm 1 thinks that Firm 2 will produce 75 units, Firm
1 will produce only 12.5 units.

Cournot equilibrium: a pair of output levels, one for
each firm, which are such that after they are choose,
neither firm has incentive to change its output level.
(Cournot equilibrium is determined by the
intersection of the reaction curves)

Reaction function: relationship between a firm’s
profit maximizing output and the amount it think its
competitor will produce

In Cournot equilibrium, each firm correctly
assumes the amount that its competitor will produce
and thereby maximizes its own profits. Therefore,
neither firm will move from this equilibrium.
Nash equilibrium: set of strategies or actions in which each firm does the best it can
given its competitors’ actions
3
Representing the Cournot duopoly game by algebra
Market demand:
p  a  (q1  q2 )
Cost functions:
c(q1 )  cq1 , c(q2 )  cq2
Firm 1 and firm 2 each faces a maximizing problem at the same time and the two firms are
symmetric. MC for both firm = c
Firm 1’s Profit function: TR  TC  pq1  cq1
Firm 1’s maximizing problem: Max  1  aq1  q12  q1q 2  cq1
0 q1 
FOC: a  2q1  q2  c  0
q1C 
(a, c are constant,
a  c  q 2C
(Firm 1’s reaction function)
2
ac
is the y-intercept of firm 1’s reaction function and slope = –1/2)
2
Firm 2’s maximizing problem: Max  2  aq2  q 22  q1q 2  cq2
0 q2  
FOC: a  2q2  q1  c  0
a  c  q1C
q 
(Firm 2’s reaction function)
2
C
2
Solving the two reaction functions for the Cournot equilibrium, it yields,
ac
2(a  c)
q1C  q2C 
、 q1C  q2C 
3
3
a

2c
pC 
3
2
 a  2c
 a  c  (a  c)
C
C
C
 c 
Profit for firm 1:  1  ( p  c)q1  

9
 3
 3 
2
 a  2c
 a  c  (a  c)
 c 

Profit for firm 2:  2C  ( p C  c)q 2C  

9
 3
 3 
Representing the Collusion by algebra
If the two firms collude, they maximize the total profit.
Market demand:
p  a  Q  a  (q1  q2 )
c(Q)  cQ
Cost functions:
The monopolist’s maximizing problem: Max   aQ  Q 2  cQ
0Q  
FOC: a  2Q  c  0
ac
ac
Q* 
q1*  q2* 
2 and
4
ac
p* 
2
(a  c) 2
 1*   2* 
8
4
Representing the Competitive model by algebra
Market demand:
p  a  Q  a  (q1  q2 )
Cost functions:
c(q1 )  cq1 , c(q2 )  cq2
In the competitive market,
p  a Q  c
QCOMP  a  c
q1COMP  q2COMP 
ac
2
p*  c
 1COMP   2COMP  0
Representing the Stackelberg duopoly game by algebra

Stakelberg model: Oligopoly model in which one firm sets its output before other firms
do
Market demand: p  a  (q1  q 2 )
Cost functions: c(q1 )  cq1 , c(q2 )  cq2
Suppose firm 1 chooses q1, firm 2 is rational. Hence firm 2 chooses q2 to solve the following
maximizing problem:
Max  2  aq 2  q 22  q1 q 2  cq2
0 q2  
FOC: a  2q 2  q1  c  0
a  c  q1S
q (q ) 
2
S
2
S
1
Firm 1 knows that firm 2 is rational, and knows if he produces q1, firm 2 will produce q2S (q1S).
Firm 1’s problem is:
Max  1  aq1  q12  q1q2S (q1S )  cq1
0 q1 
aq1  cq1  q12
 cq1
0  q1  
2
FOC: a  2q1  12 (a  c  2q1 )  c  0
Max  1  aq1  q12 
a  c  q1S a  c
ac

, q2S (q1S ) 
2
4
2
a

3
c
p S  a  (q1  q 2 ) 
4
2
 a  3c
 a  c  (a  c)
 c 

Profit for firm 1:  1S  ( p S  c)q1S  

8
 4
 2 
q1S 
2
 a  3c
 a  c  (a  c)
 c 

Profit for firm 2:  2S  ( p S  c)q 2S  

16
 4
 4 
5
Representing the monopoly game by algebra
Market demand:
p  a  QM
Cost functions:
c(QM) = cQM
The monopolist’s maximizing problem: Max  M  aQM  QM2  cQM
0QM 
FOC: a  2QM  c  0
ac
QM* 
2
ac
p M* 
2
2
ac
 a  c  (a  c)
*
*
*
 M  ( p M  c)QM  
 c 

4
 2
 2 
Welfare properties of duopolistic markets and comparisons
Comparing prices, quantities and profit with algebra
Price
Monopoly
Cournot
Stackelberg
Bertrand
ac
2
a

2c
pC 
3
a  3c
pS 
4
p M* 
pB  c
Firm 1’s output
ac
2
a

c
q1C 
3
ac
q1S 
2
a
c
B
q1 
2
Firm 2’s output
QM* 
Industry output
ac
3
ac
q 2S (q1S ) 
4
ac
B
q2 
2
Firm 2’s profit
ac
2
2
(
a  c)
QC 
3
3(a  c)
QS 
4
(a  c)
4
(a  c) 2
 1C 
9
(
a

c) 2
 1S 
8
( a  c) 2
9
(
a

c) 2
 2S 
16
Q B  (a  c)
 1B  0
 2B  0
QM* 
q 2C 
Firm 1’s profit
 M* 
2


In the above analysis, assume a > c, since quantities of output must be positive.
p M  pC  p S  p B


Q B  Q S  QC  Q M
S
 M   leader
  iC1, 2   Sfollower   B
 2C 

–
–
Comparing Cournot and Stackelberg equilibrium:
In the Cournot model, both firms choose quantities simultaneously.
In the Stackelberg game, one firm will be the leader and the other will be the follower,
they move sequentially, there is always a first mover advantage.
 p C  p S , QC  Q S
–
For Firm 1,
ac
ac
 q1C 
2
3
2
2
  1S  (a  c)   1C  (a  c)
8
9
 q1S 
–
For Firm 2,
 q 2C  a  c  q2S (q1S )  a  c
  2C
3
4
2
( a  c)
(a  c) 2

  2S 
9
16
6
Comparing consumer surplus, producer surplus and DWL
Welfare is measured in terms of consumer surplus and producer surplus
Cournot equilibrium outputs are in between the two extremes of monopoly and perfect
competition
P
DWL under
monopoly
p M* 
ac
2
DWL under
Cournot duopoly
a  2c
3
p COMP  p B  c
pC 
MC = c
DD :
MR
ac
Q 
2
*
M
QC 
p=a–Q
QCOMP  Q B  (a  c)
Q
2(a  c)
3


Market demand: p = a – Q
Marginal cost: c







Perfectly competitive market
In the perfectly competitive market, firm’s output is welfare maximizing quantity
Consumer surplus is maximized
No producer surplus as price is equal to MC
Total surplus maximized
No DWL
The result is the same in Bertrand duopoly





Monopoly
Firm’s output is lower which is not welfare optimal
Price is higher than the competitive price and the Cournot price
CS falls and PS rises
Total surplus is not maximized, and there exists a DWL
 Cournot duopoly
 The price and quantity is between perfectly competitive market and monopoly
 The Cournot equilibrium quantity is still not welfare optimal, it is better than monopoly,
but worse than perfectly competitive market.
 Stackelberg duopoly
 The price and quantity is between perfectly competitive market and Cournot equilibrium.
 The Stackelberg equilibrium quantity is still not welfare optimal, it is better than
monopoly, but worse than perfectly competitive market. (It’s also better than Cournot
equilibrium)
7
Comparing equilibrium price and quantity with iso-output line
Output of
firm 2
q2
ac
COMP
Reaction function for firm 1
q1  f 1 (q 2 )
2(a  c)
3
q2 
QM* 
Welfare optimal output
q1  q2  a  c
ac
2
Cournot output
q1  q2 
ac
q 
3
C
2
E
Reaction function for firm 2
q 2  f 2 (q1 )
Monopoly output
q1  q2 
2(a  c)
3
ac
2
Output of
firm 1
q1C 
ac
3
QM* 
ac
2
q1
q1 
COMP
2(a  c)
3
ac
(monopoly output)
2
 a  c (competitive output), the optimal response for firm 1 is 0

When q2 = 0, the optimal response for firm 1 is QM* 

When q2 = q1

When q1 = 0, the optimal response for firm 2 is QM* 

When q1 = q1
C
ac
C
ac
2
 a  c , the optimal response for firm 2 is 0

Iso-output line: different combinations of q1 and q2 give the same amount of total output
at same price level
 Since price level depends on the total output, as the total output level is constant over all
the output combinations on the same iso-product line, price level is constant on an
iso-product line.
 Point E is the Cournot equilibrium
 Cournot equilibrium quantity is on an iso-output line strictly between the monopoly line
and the welfare optimal line
 At Cournot equilibrium, price and quantity are between the monopoly and welfare
optimal levels
 The outcome for society between the monopoly and welfare optimal levels
8
Numerical Example:
Let there be 2 firms, A and B, in a market of the same good
MC = 2 for both Firm A and Firm B
The demand function of the market is given by P  26  q A  q B 
Cournot Model
Scenario 1: Cournot equilibrium
Firm A’s profit maximizing problem:
Max A  (26  q A  q B )q A  2q A
qA
FOC: 24  2q A  q B  0
q
q *A  12  B (Reaction function for firm A)
2
Firm B’s profit maximizing problem:
Max B  (26  q A  q B )q B  2q B
qB
FOC: 24  2q B  q A  0
q
q B*  12  A (Reaction function for firm B)
2
Solving the two reaction functions for the Cournot equilibrium:
q*A  qB*  8 and p*  10
Profit for firm A  p * q *A  10(8)  2(8)  64
Profit for firm B  p * q B*  10(8)  2(8)  64
Scenario 2: Cartel
If Firm A and Firm B collude, they will act as a monopoly and will maximize the joint profit.
Their joint maximization problem:
Max  (26  Q)Q  2Q
Q
FOC: 24  2Q  0
Q* = 12, q *A  q B*  6
p *  14
Profit for firm A  p * q *A  14(6)  2(6)  72
Profit for firm B  p * q B*  14(6)  2(6)  72

The total profit Cartel is higher (monopoly profit = 72 + 72) than the total profit in
Cournot equilibrium (total profit = 64 + 64).
9
Cartel and stability
Cartel is not stable. We could show that both firms will have incentive to depart from the
collusion. In the end, they will act independently with the equilibrium as in the case of
oligopoly (Cournot equilibrium).
In the Cartel, q *A  q B*  6 . Both firms will have incentive to increase production for a higher
profit, given the other firm follow the cartel.
Scenario 3: One of the firm deviates
Suppose Firm B follows the cartel and produces q B*  6 .
According to the Reaction function of Firm A,
q
q *A  12  B  9
2
p* = 26 – (qA + qB) = 26 – 6 – 9 =11
Profit for firm A  p * q *A  11(9)  2(9)  81
Profit for firm B  p * q B*  11(6)  2(6)  54
Firm B will also have incentive to deviate from the cartel too.
Scenario 4: Both of the firms deviate
If both firm A and B deviate and q *A  9 , q B*  9 , p* = 26 – 9 – 9 = 8
Profit for each firm = 54

From the above example, we could show that the cartel is not stable, both of them will
deviate and it end up in the Cournot equilibrium again. We could analysis the scenario
by game theory and represent it with a payoff matrix. (In fact, it is a Prisoner’s dilemma
game)
Comparison of equilibrium

Price
Firm A’s
output
Firm B’s
output
Industry
output
Firm A’s
profit
Firm B’s
profit
Cournot
p*  10
q*A  8
qB*  8
Q = 16
 A  64
 B  64
Cartel
p *  14
q*A  6
qB*  6
Q = 12
 A  72
 B  72
One firm (A)
deviates
Both firm
deviate
p*  11
q*A  9
qB*  6
Q = 15
 A  81
 B  54
p*  8
q*A  9
qB*  9
Q = 18
 B  54
 B  54
Profit under Cartel is the highest, however, as the cartel is not stable, firms will deviate
and end up in Cournot equilibrium. (Profit for each firm 72 > 64)
10
Stackelberg Model
Suppose firm 1 chooses q1, firm 2 is rational. Hence firm 2 chooses q2 to solve the following
maximizing problem:
Max B  (26  q A  q B )q B  2q B
qB
FOC: 24  2q B  q A  0
q AS
q (q )  12 
2
*
B
S
A
Firm 1 knows that firm 2 is rational, and knows if he produces q1, firm 2 will produce qBS
(qAS). Firm 1’s problem is: Max A  [26  q A  q BS (q AS )]q A  2q A
qA
FOC: 26  2q A  12  q A  2  0
q*A  12 , qB*  6 and p *  8
Profit for firm A:  A  ( p*  c)q1*  72 . Profit for firm B:  B  ( p*  c)q2*  36
Bertrand Model
p*  MC  2 . p  26  q A  q B  , q A  q B  12 ,  A   B  0
Monopoly
The monopolist’s maximizing problem: Max  (26  qM )qM  2qM
qM
FOC: 26  2qM  2  0
qM*  12 ,
p*  14 and  M  144
11