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!!!
Wireless (2002)
US Beer (2001)
Music Recording (2001)
Verizon: 30%
Cingular: 22%
AT&T: 20%
Sprint PCS: 14%
Nextel: 10%
Voicestream: 6%
Anheuser-Busch: 49%
Miller: 20%
Coors: 11%
Pabst: 4%
Heineken: 3%
Universal/Polygram: 23%
Sony: 15%
EMI: 13%
Warner: 12%
BMG: 8%
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
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!
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
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
Q P
1  53.33 

 
  1.6
P Qi
20  1.67 
MC
p
 1
1  
 
$20
$53.33 
1 

1 

 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 
MC
p
 1
1  
 
$20
$70 
1 

1 

 1 .4 
Had this market been instead perfectly competitive,
P  120  20Q
MC  $20
Q*  5M
P  120  20(2.5)  $20
  
MC
p
 1
1  
 
$20
$20 
 1
1  
 
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
CS = (.5)(120 – 53)(3.33) = $112
p
Q  3.33M
q  1.67
P  $53
$112
$53
LI  .62
HHI  5,000
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
LI  .55
HHI  3,267
$140
$45
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
 1  56.81.83  201.83  67.34
q2
 2  56.81.33  301.33  35.64
Firm 1
HHI  42 2  582  5128
LI  .65
q2  1.33
42%
Firm 2
q  1.83
*
1
58%
q1
Firm 2’s market share drops
Firm 1’s Market Share increases
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
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

Firm 1 profit
maximizes by choice
of price
p1  30  .5 p2
Each firm needs to choose
price to maximize profits
conditional on the other
firm’s choice of price.
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
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
Best response strategies are strategic complements
Bertrand
p2
Cournot
q2
Firm 1
Firm 1
Firm 2
Firm 2
p1
q1
Stackelberg leadership
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
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 2 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
Perfect
Competition
q2  .62
Q*  5M
P  $75
LI  .73
HHI  5,288
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.