Transcript Finance 510: Microeconomic Analysis

Finance 30210: Managerial
Economics
Strategic Pricing Techniques
Recall that there is an entire spectrum of market
structures
Market Structures
Perfect Competition
Monopoly
Many firms, each with zero
One firm, with 100%
market share
market share
P = MC
Profits = 0 (Firm’s earn a
P > MC
Profits > 0 (Firm’s earn
reasonable rate of return on
invested capital)
excessive rates of return
on invested capital)
NO STRATEGIC
NO STRATEGIC
INTERACTION!
INTERACTION!
Most industries, however, don’t fit the assumptions of either perfect
competition or monopoly. We call these industries oligopolies
Oligopoly
Relatively few firms, each
with positive market share
STRATEGIES MATTER!!!
Mobile Phones
(2011)
Nokia: 22.8%
Samsung: 16.3%
LG: 5.7%
Apple: 4.6%
ZTE:3.0%
Others: 47.6%
US Beer (2010)
Music Recording (2005)
Anheuser-Busch: 49%
Miller/Coors: 29%
Crown Imports: 5%
Heineken USA: 4%
Pabst: 3%
Universal/Polygram: 31%
Sony: 26%
Warner: 25%
Independent Labels: 18%
The key difference in oligopoly markets is that price/sales decisions can’t
be made independently of your competitor’s decisions
Monopoly
Q  QP
Your Price (-)
Oligopoly
Q  QP, P1 ,...PN 
Your N Competitors
Prices (+)
Oligopoly markets rely crucially on the interactions between
firms which is why we need game theory to analyze them!
Market shares are not constant over time in these industries!
Airlines (1992)
Airlines (2002)
American
21
United
20
15
Delta
Northwest
Continental 11
US Air
9
14
American
19
United
17
15
Delta
Northwest
11
Continental 9
SWest
7
While the absolute ordering didn’t change, all the airlines lost
market share to Southwest.
Another trend is consolidation
Retail Gasoline (1992)
9
Shell
Chevron
8
8
8
Texaco
Exxon
Amoco
7
7
Mobil
5
5
4
4
24
Exxon/Mobil
Shell
20
BP/Amoco/Arco 18
Chev/Texaco 16
10
6
BP
Citgo
Marathon
Sun
Phillips
Retail Gasoline (2001)
7
Total/Fina/Elf
Conoco/Phillips
Recall the prisoners dilemma game…
Clyde
Jake
The prisoner’s dilemma game
is used to describe
circumstances where
competition forces suboptimal outcomes
Confess Don’t
Confess
Confess -4 -4
0 -8
Don’t
Confess
-8
0
-1
-1
Price Fixing and Collusion
Prior to 1993, the record fine in the United States for price fixing was
$2M. Recently, that record has been shattered!
Defendant
Product
Year
Fine
F. Hoffman-Laroche
Vitamins
1999
$500M
BASF
Vitamins
1999
$225M
SGL Carbon
Graphite Electrodes
1999
$135M
UCAR International
Graphite Electrodes
1998
$110M
Archer Daniels Midland
Lysine & Citric Acid
1997
$100M
Haarman & Reimer
Citric Acid
1997
$50M
HeereMac
Marine Construction
1998
$49M
In other words…Cartels happen!
Suppose that we have two firms in the market. They face the following
demand curve…
Each has a marginal
cost of $80.
P  400  4q1  q2 
Firm 1’s output
Firm 2’s output
If these firms formed a cartel, they would operate jointly as a monopolist.
P  400  4Q
MR  400  8Q  80  MC
Each firm agrees
to sell 20 units at
$240 each.
  240  8020  $3,200
Q  40
P  $240
Each firm makes $3200
in profits
However, given that firm 2 is producing 20 units, what should firm 1 do?
P  400  4q1  20
Firm 1’s output
P  400  4q1  80
Firm 2’s output
P  400  430  20  $200
P  320  4q1  80
MR  320  8q1  80  MC
Q  30
1  200  8030  $3,600
2  200  8020  $2,400
Firm 1 cheats and earns more
profits!
But if they both cheat and produce 30 units…
P  400  430  30  $160
1  160  8030  $2,400
2  160  8030  $2,400
Cartels - The Prisoner’s Dilemma
The problem facing the cartel members is
a perfect example of the prisoner’s
dilemma !
Clyde
Cooperate
Jake
Cheat
Cooperate
$3200 $3200
$2400
$3600
Cheat
$3600
$2400
$2400
$2400
Cheating is a dominant strategy!
Cartel Formation
While it is clearly in each firm’s best interest to join the cartel, there
are a couple problems:
With the high monopoly markup, each firm has the incentive to
cheat and overproduce. If every firm cheats, the price falls and
the cartel breaks down
Cartels are generally illegal which makes enforcement difficult!
Note that as the number of cartel members increases the
benefits increase, but more members makes enforcement even
more difficult!
Perhaps cartels can be
maintained because the
members are interacting over
time – this brings is a possible
punishment for cheating.
Clyde
Cooperate
Cheat
Cooperate
$3200 $3200
$2400
$3600
Cheat
$3600
$2400
$2400
Jake
Jake
“I plan on cooperating…if you cooperate today, I will cooperate
tomorrow, but if you cheat today, I will cheat forever!”
0
1
Make Strategic
Decision
Make Strategic
Decision
Time
$2400
2
Make Strategic
Decision
3
Make Strategic
Decision
4
Make Strategic
Decision
5
Make Strategic
Decision
“I plan on cooperating…if you
cooperate today, I will cooperate
tomorrow, but if you cheat today, I will
cheat forever!”
Jake
Cooperate:
$3200
Cooperate
Cheat
Cooperate
$3200 $3200
$2400
$3600
Cheat
$3600
$2400
$2400
$2400
$3200
$3200
$3200
$3200
$3200
0
1
2
3
4
5
Make Strategic
Decision
Make Strategic
Decision
Clyde
Time
Cheat:
$3600
Cooperate: $19,200
Cheat: $15,600
$2400
Make Strategic
Decision
$2400
Make Strategic
Decision
$2400
Make Strategic
Decision
Make Strategic
Decision
$2400
$2400
Clyde should cooperate, right?
We need to use backward
induction to solve this.
0
1
Make Strategic
Decision
Make Strategic
Decision
Time
Jake
2
Make Strategic
Decision
3
Clyde
4
Make Strategic
Decision
5
Make Strategic
Decision
Cooperate
Regardless of what took place the
first four time periods, what will
happen in period 5?
Make Strategic
Decision
Cheat
Cooperate
$3200 $3200
$2400
$3600
Cheat
$3600
$2400
$2400
$2400
What should
Clyde do here?
We need to use backward
induction to solve this.
0
1
Make Strategic
Decision
Make Strategic
Decision
Time
Jake
2
3
Make Strategic
Decision
Clyde
4
Make Strategic
Decision
Make Strategic
Decision
5
Make Strategic
Decision
Cheat
Cooperate
Given what
happens in period
5, what should
happen in period 4?
Cheat
Cooperate
$3200 $3200
$2400
$3600
Cheat
$3600
$2400
$2400
$2400
What should
Clyde do here?
We need to use backward
induction to solve this.
0
1
Make Strategic
Decision
Make Strategic
Decision
Time
Jake
2
Make Strategic
Decision
Cheat
Cooperate
Cheat
Make Strategic
Decision
Cheat
Cheat
Cooperate
$3200 $3200
$2400
$3600
Cheat
$3600
$2400
$2400
$2400
3
Knowing the future prevents credible
promises/threats!
4
Make Strategic
Decision
Cheat
Clyde
5
Make Strategic
Decision
Cheat
Where is collusion most likely to occur?
High profit potential
Inelastic Demand (Few close substitutes, Necessities)
Cartel members control most of the market
Entry Restrictions (Natural or Artificial)
Low cooperation/monitoring costs
Small Number of Firms with a high degree of market
concentration
Similar production costs
Little product differentiation
Price Matching: A form of collusion?
High Price
Low Price
High Price
$12 $12
$5
$14
Low Price
$14
$6
$6
$5
Price Matching Removes the off-diagonal possibilities. This
allows (High Price, High Price) to be an equilibrium!!
The Stag Hunt - Airline Price
Wars
p
Suppose that American and Delta
face the given demand for flights to
NYC and that the unit cost for the
trip is $200. If they charge the same
fare, they split the market
$500
$220
American
180
What will the equilibrium
be?
P = $220
P = $500
$9,000
$9,000
$3,600
$0
P = $220
$0
$3,600
$1,800
$1,800
Q
Delta
60
P = $500
The Airline Price Wars
If American follows a strategy of charging $500 all the time, Delta’s best
response is to also charge $500 all the time
If American follows a strategy of charging $220 all the time, Delta’s best
response is to also charge $220 all the time
American
P = $220
P = $500
$9,000
$9,000
$3,600
$0
P = $220
$0
$3,600
$1,800
$1,800
Delta
This game has multiple
equilibria and the result depends
critically on each company’s
beliefs about the other
company’s strategy
P = $500
The Airline Price Wars: Mixed Strategy Equilibria
Suppose American charges $500 with probability pH
Charges $220 with probability
pL
Charge $500: EV   pH 9000   pL 0
Charge $220:EV   pH 3600  PL 1800
American
P = $500
P = $220
$9,000
$9,000
$3,600
$0
9000 pH  3600 pH  1800 pL
Delta
P = $500
pL  3 pH
(6%)
P = $220
$0
$3,600
(19%)
pL 
3
(75%)
4
pH 
1
(25%)
4
(19%)
$1,800
$1,800
(56%)
Continuous Choice Games
Consider the following example. We have two competing firms in
the marketplace.
These two firms are selling identical products.
 Each firm has constant marginal costs of production.
What are these firms using
as their strategic choice
variable? Price or quantity?
Are these firms making their
decisions simultaneously or
is there a sequence to the
decisions?
Cournot Competition: Quantity is the strategic choice variable
There are two firms in an industry – both
facing an aggregate (inverse) demand
curve given by
p
P  120  20Q
D
Q
Total
Industry
Production
Q  q1  q2
Both firms have constant marginal costs equal to $20
Consider the following scenario…We call this Cournot competition
Two manufacturers
choose a production
target
Two manufacturers
earn profits based
off the market price
P
Q1
S
P*
Profit = P*Q1 - TC
D
Q
Q1 + Q2
Q2
A centralized market
determines the market price
based on available supply and
current demand
Profit = P*Q2 - TC
For example…suppose both firms have a constant marginal cost of $20
Two manufacturers
choose a production
target
P  120  20Q
P
Q1 = 1
Two manufacturers
earn profits based
off the market price
S
$60
Profit = 60*1 – 20 = $40
D
Q
3
Q2 = 2
A centralized market
determines the market price
based on available supply and
current demand
Profit = 60*2 – 40 = $80
From firm one’s perspective, the demand curve is given by
P  120  20q1  q2   120  20q2   20q1
Treated as a constant by Firm One
Solving Firm One’s Profit Maximization…
MR  120  20q2   40q1  20
100  20q2
q1 
40
100  20q2
q1 
40
In Game Theory Lingo, this is Firm One’s Best
Response Function To Firm 2
q2
If firm 2 drops out, firm
one is a monopolist!
P  120  20q1
MR  120  40q1  20
q1  2.5
0
q2  0
q1  2.5
q1
100  20q2
q1 
40
What could firm 2 do to
make firm 1 drop out?
q2
P  120  205  20  MC
q2  5
q1  0
q2  0
q1  2.5
q1
P  120  20Q
q2
100  20q2
q1 
40
P  120  204  40
q2  5
q1  0
Firm 2
chooses a
production
target of 3
3
1
Firm 1
responds
with a
production
target of 1
q2  0
q1  2.5
q1
 1  401  201  20
 2  403  203  60
The game is symmetric with respect to Firm two…
P  120  20Q
q2
100  20q1
q2 
40
P  120  203  60
q1  0
q2  2.5
Firm 2
responds
with a
production
target of 2
q1  5
q2  0
Firm 1 chooses a
production target of
1
q1
 1  601  201  40
 2  602  202  80
Eventually, these two firms converge on production levels such that
neither firm has an incentive to change
100  20q2
q1 
40
q2
100  20q1
q2 
40
100  201.67 
1.67 
40
Firm 1
We would call this the
Nash equilibrium for
this model
q2*  1.67
Firm 2
q1*  1.67
q1
Recall we started with the demand curve and marginal costs
P  120  20Q
MC  20
q1*  q2*  1.67M
P  120  20(3.33)  $53.33
 1  53.331.67   201.67   $55.66
 2  53.331.67   201.67   $55.66
The markup formula works for each firm
P  120  20q2   20q1  86.6  20q1
MC  $20
Q*  1.67 M
P  86.6  20(1.67)  $53.33
P  MC
 .62
P
1
Q P
1  53.33 

 
  1.6
P Qi
20  1.67 
1

 .62
 1.6
Had this market been serviced instead by a monopoly…
P  120  20Q
MC  $20
Q*  2.5M
P  120  20(2.5)  $70
Q P
1  70 

 
  1.4
P Q
20  2.5 
P  MC
 .71
P
1
1

 .71
 1.4
Had this market been instead perfectly competitive,
P  120  20Q
MC  $20
Q*  5M
P  120  20(2.5)  $20
  
P  MC
0
P
1
1
 0
 
P  120  20Q
MC  $20
Monopoly
Q*  2.5M
P  $70
LI  .71
HHI  10,000
2 Firms
Q  3.33M
q  1.67
P  $53
LI  .62
HHI  5,000
Perfect
Competition
Q*  5M
P  $20
LI  0
HHI  0
Recall, we had an aggregate demand and a constant marginal cost of
production.
P  120  20Q
MC  $20
Monopoly
Q*  2.5M
P  $70
LI  .71
HHI  10,000
CS = (.5)(120 – 70)(2.5) = $62.5
p
$120
$62.5
$70
D
What would it be worth to consumers to
add another firm to the industry?
2.5
Q
Recall, we had an aggregate demand and a constant marginal cost of
production.
P  120  20Q
MC  $20
Two Firms
Q  3.33M
q  1.67
P  $53
LI  .62
HHI  5,000
CS = (.5)(120 – 53)(3.33) = $112
p
$112
$53
D
3.33
Q
Suppose we increase the number of firms…say, to 3
P  120  20q1  q2  q3 
P  120  20Q
Demand facing firm 1 is given by (MC = 20)
P  120  20q2  20q3   20q1
MR  120  20q2  20q3   40q1  20
q1 
100  20q2  20q3
40
The strategies look very similar!
With three firms in the market…
P  120  20Q
MC  $20
CS = (.5)(120 – 45)(3.75) = $140
Three Firms
p
qi  1.25M
Q  3q  3.75
P  $45
$140
$45
LI  .55
HHI  3,267
D
3.75
Q
Expanding the number of firms in an oligopoly – Cournot Competition
P  A  BQ
MC  c
Ac
qi 
( N  1) B
N A  c
Q
( N  1) B
A
 N 
P

c
N 1  N 1
N = Number of firms
Note that as the number of firms increases:
Output approaches the perfectly competitive level of production
Price approaches marginal cost.
Increasing Competition
6
80
70
5
60
4
50
3
40
30
2
20
1
10
0
0
Number of Firms
Firm Sales
Industry Sales
Price
Increasing Competition
300
250
200
150
100
50
Num ber of Firm s
Consumer Surplus
Firm Profit
Industry Profit
97
93
89
85
81
77
73
69
65
61
57
53
49
45
41
37
33
29
25
21
17
13
9
5
1
0
The previous analysis was with identical firms.
P  120  20Q
MC  $20
100  20q2
q1 
40
100  20q1
q2 
40
Suppose Firm 2’s marginal costs
increase to $30
q2
Firm 1
q2*  1.67
50%
Firm 2
q1*  1.67 50%
q1
P  120  20Q
MC  $30
q2
Suppose Firm 2’s marginal costs
increase to $30
P  120  20q1   20q2
MR  120  20q1   40q2  30
90  20q1
q2 
40
If Firm one’s production is
unchanged
90  201.67 
q2 
 1.41
40
q2*  1.67
1.41
Firm 2
q1*  1.67
q1
90  20q1
100  20q2
q2 
q1 
40
40
Q  1.33  1.83  3.16
P  120  203.16   $56.8
q2
 1  56.81.83  201.83  67.34
 2  56.81.33  301.33  35.64
Firm 1
HHI  42 2  582  5128
P  MC
 .56
MC
q2  1.33
42%
Firm 2
q  1.83
*
1
58%
q1
Firm 2’s market share drops
Firm 1’s Market Share increases
Market Concentration and Profitability
N
P  A  B  qi
Industry Demand
i 1
P  MC si

P

 HHI 


P  MC  10, 000 

P

The Lerner index for Firm i is related
to Firm i’s market share and the
elasticity of industry demand
The Average Lerner index for the
industry is related to the HHI and the
elasticity of industry demand
P  120  20Q
MC1  20
q1  1.83
(58%)
q2  1.33
(42%)
MC2  $30
HHI  42 2  582  5128
Industry

Q P
1  56.80 
 
  .90
P Qi
20  3.16 
 HHI 


 10,000   .5128  .56

.90
P  $56.80
P  MC
 .56
MC
Firm 1
P  MC 56.80  20
.58

 .64 
P
56.80
.90
Firm 2
P  MC 56.80  30
.42

 .47 
P
56.80
.90
The previous analysis (Cournot Competition) considered quantity as the
strategic variable. Bertrand competition uses price as the strategic variable.
p
Should it matter?
P*
D
Q*
P  120  20Q
Industry Output
Q
Just as before, we have an
industry demand curve and two
competing duopolies – both with
marginal cost equal to $20.
Firm level demand curves look very different when we change strategic
variables
Bertrand Case
Quantity Strategy
Q  6  .05 P
P  120  20q2   20q1
p
p1
120  20q2 
p2
D
q1
If you are
underpriced, you lose
the whole market
At equal
prices, you
split the
market
D
q1
If you are
the low
price you
capture the
whole
market
Price competition creates a discontinuity in each firm’s demand curve –
this, in turn creates a discontinuity in profits
if p1  p2
 0



 6  .05 p1 
 1  p1 , p2   ( p1  20)
 if p1  p2
2




 ( p  20)(6  .05 p ) if p  p
1
1
2
 1
As in the cournot case, we need to find firm one’s best response
(i.e. profit maximizing response) to every possible price set by firm 2.
Firm One’s Best Response Function
Case #1: Firm 2 sets a price above the pure monopoly price:
p2  pm
p1  pm
Case #2: Firm 2 sets a price between the monopoly price and marginal cost
pm  p2  20
p1  p2  
Case #3: Firm 2 sets a price below marginal cost
20  p2
p1  p2
Case #4: Firm 2 sets a price equal to marginal cost
c  p2
p1  p2  c
What’s the Nash equilibrium of this game?
Monopoly
Q*  2.5M
P  $70
LI  2.5
HHI  10,000
2 Firms
Q  5M
q  2 .5
P  $20
LI  0
HHI  5,000
Perfect
Competition
Q*  5M
P  $20
LI  0
HHI  0
However, the Bertrand equilibrium makes some very restricting
assumptions…
Firms are producing identical products (i.e. perfect
substitutes)
Firms are not capacity constrained
An example…capacity constraints
Consider two theatres located side by side. Each theatre’s marginal cost is
constant at $10. Both face an aggregate demand for movies equal to
Q  6,000  60 P
Each theatre has the capacity to handle 2,000 customers per day.
What will the equilibrium be in this case?
Q  6,000  60 P
If both firms set a price equal to $10
(Marginal cost), then market demand is
5,400 (well above total capacity = 2,000)
Note: The Bertrand Equilibrium (P = MC) relies on each firm having the ability
to make a credible threat:
“If you set a price above marginal cost, I will
undercut you and steal all your customers!”
4,000  6,000  60P
P  $33.33
At a price of $33, market demand is 4,000 and both firms operate at capacity. Now,
how do we choose capacity? Back to Cournot competition!
With competition in price, the key is to create product variety somehow!
Suppose that we have two firms. Again, marginal costs are $20. The two
firms produce imperfect substitutes.
 p  p1  40 
q1   2

80


Example:
 p1  p2  40 
q2  

80


p2  40
p
80
q1  1  .0125 p1 
D
q1
Recall Firm 1 has a marginal cost of $20

1  ( p1  20)

p2  p1  40 

80

Each firm needs to choose
price to maximize profits
conditional on the other
firm’s choice of price.
q1
Firm 1 profit
maximizes by choice
of price
p1  30  .5 p2
p2
Firm 2 sets
a price of
$50
Firm 1’s strategy
D
$30
Firm 1 responds
with $55
p1
With equal costs, both firms set the same
price and split the market evenly
p1  30  .5 p2
p2  30  .5 p1
p2
Firm 1
Firm 2
$60
$30
$30
$60
p1
q1  .50
p1  $60
q2  .50
p2  $60
Monopoly
Q*  2.5M
P  $70
LI  .71
HHI  10,000
2 Firms
P  $60
LI  .66
HHI  5,000
Perfect
Competition
Q*  5M
P  $20
LI  0
HHI  0
Suppose that Firm two‘s costs increase. What happens in each case?
 p1  p2  40 
 2  ( p2  20)

80


Bertrand
p2
Firm 2
$30
p1
With higher marginal
costs, firm 2’s profit
margins shrink. To
bring profit margins
back up, firm two raises
its price
Suppose that Firm two‘s costs increase. What happens in each case?
p2
With higher marginal
costs, firm 2’s profit
margins shrink. To
bring profit margins
back up, firm two raises
its price
Firm 1
Firm 2
p1
A higher price from firm
two sends customers to
firm 1. This allows firm
1 to raise price as well
and maintain market
share!
Cournot (Quantity Competition): Competition is for market share
Firm One responds to firm 2’s cost increases by expanding production and increasing
market share – prices are fairly stable and market shares fluctuate
Best response strategies are strategic substitutes
Bertrand (Price Competition): Competition is for profit margin
Firm One responds to firm 2’s cost increases by increasing price and maintaining market
share – prices fluctuate and market shares are fairly stable.
Best response strategies are strategic complements
Bertrand
p2
Cournot
q2
Firm 1
Firm 1
Firm 2
Firm 2
p1
q1
Stackelberg leadership – Incumbent/Entrant type games
In the previous example, firms made price/quantity decisions simultaneously.
Suppose we relax that and allow one firm to choose first.
P  120  20Q
MC  20
Both firms have a marginal cost equal to $20
Firm 1 chooses
its output first
Firm 2 chooses its
output second
Market Price is
determined
Firm 2 has observed Firm 1’s output decision and faces the
residual demand curve:
P  120  20q1   20q2
q2
q2  5
q1  0
MR  120  20q1   40q2  20
100  20q1
q2 
40
q2  0
q1  2.5
q1
Firm 2’s
strategy
Knowing Firm 2’s response, Firm 1 can now maximize its profits:
P  120  20q2   20q1
100  20q1
q2 
40
P  70  10q1
MR  70  20q1  20
q1  2.5
Firm 1 produces
the monopoly
output!
q1  2.5
100  20q1
q2 
 1.25
40
Q  3.75
P  120  203.75  $45
 1  452.5  202.5  62.50
 2  451.25  201.25  31.25
2 Firms
Monopoly
Q*  2.5M
P  $70
LI  .71
HHI  10,000
Q  3.75M
q1  2.5 (67%)
q2  1.25
(33%)
P  $45
LI  .55
HHI  5,587
Perfect
Competition
Q*  5M
P  $20
LI  0
HHI  0
Sequential Bertrand Competition
We could also sequence events using price competition.
 p2  p1  40 
q1  

80


 p1  p2  40 
q2  

80


Both firms have a marginal cost equal to $20
Firm 1 chooses its
price first
Firm 2 chooses its
price second
Market sales are
determined
Recall Firm 1 has a marginal cost of $20
 p2  p1  40 
1  ( p1  20)

80


p2  30  .5 p1
From earlier, we know the
strategy of firm 2. Plug this into
firm one’s profits…
  .5 p1  70 
1  ( p1  20)

80


Now we can maximize profits
with respect to firm one’s price.
Sequential Bertrand Competition
p1  $80
p2  $70
q1  .38
q2  .62
2 Firms
Monopoly
Q*  2.5M
P  $70
LI  .71
HHI  10,000
q1  .38
q2  .62
P  $75
LI  .73
HHI  5,288
Perfect
Competition
Q*  5M
P  $20
LI  0
HHI  0
Cournot vs. Bertrand: Stackelberg Games
Cournot (Quantity Competition):

Firm One has a first mover advantage – it gains market share and
earns higher profits. Firm B loses market share and earns lower
profits

Total industry output increases (price decreases)
Bertrand (Price Competition):
Firm Two has a second mover advantage – it charges a lower price
(relative to firm one), gains market share and increases profits.
Overall, production drops, prices rise, and both firms increase profits.
Predatory Pricing: A pricing strategy that makes sense only if it drives a
competitor out of business.
Suppose that a Cournot competitor decides to exploit the first mover advantage
to drive its competitor out of business…
P  120  20Q
MC  20
Both firms have a marginal cost equal to $20, each also has a fixed
cost equal to $5
Firm 1 chooses its
output first
Firm 2 chooses its
output second
Market Price is
determined
Knowing Firm 2’s response, We can adjust the demand curve:
P  120  20q2   20q1
100  20q1
q2 
40
P  70 10q1
This demand curve incorporates firm two’s behavior.
Now, we want to create firm 2’s profits:
2  P  MC q2  FC
 100  20q1 
 2  70  10q1  20
5
40


100  20q1
q2 
40
P  70 10q1
MC = $20, FC = $5
 100  20q1  1 
 2  50  10q1 
   5
2

 20 
 2  50  10q1 
2
 1 
 5
 20 
We want to find the level of production by firm 1 that lowers Firm 2’s
profits to zero…
 2  50  10q1 
2
 1 
 5  0
 20 
50  10q1 
2
 100
50 10q1  10
q1  4
100  20q1
q2 
 .5
40
P  70 10q1  30
Now, we can calculate profits…
1  P  MC q1  FC
1  30  204  5  35
q1  4
q2  .5
P  30
2  P  MC q2  FC
 2  30  20.5  5  0
Note: This was by design!
Firm one sacrifices some profits today to stay a monopoly!
There have been numerous cases involving predatory pricing
throughout history.
Standard Oil
American Sugar Refining Company
Mogul Steamship Company
Wall Mart
AT&T
Toyota
American Airlines
There are two good reasons why we would most likely not see predatory
pricing in practice
1. It is difficult to make a credible threat (Remember the Chain
Store Paradox)!
2. A merger is generally a dominant strategy!!
The Bottom Line with Predatory Pricing…
There have been numerous cases over the years alleging predatory
pricing. However, from a practical standpoint we need to ask three
questions:
1. Can predatory pricing be a rational strategy?
2. Can we distinguish predatory pricing from
competitive pricing?
3. If we find evidence for predatory pricing, what do
we do about it?