Economics of the Firm
Strategic Pricing Techniques
Recall that there is an entire spectrum of market
structures
Market Structures
Perfect Competition
Many firms, each with zero
market share
P = MC
Profits = 0 (Firm’s earn a
reasonable rate of return on
invested capital)
NO STRATEGIC
INTERACTION!
Monopoly
One firm, with 100%
market share
P > MC
Profits > 0 (Firm’s earn
excessive rates of return
on invested capital)
NO STRATEGIC
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)
Verizon: 30%
Cingular: 22%
AT&T: 20%
Sprint PCS: 14%
Nextel: 10%
Voicestream: 6%
US Beer (2001)
Anheuser-Busch: 49%
Miller: 20%
Coors: 11%
Pabst: 4%
Heineken: 3%
Music Recording (2001)
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!
Prisoner’s Dilemma…A Classic!
Two prisoners (Jake & Clyde) have been arrested. The DA
has enough evidence to convict them both for 1 year, but
would like to convict them of a more serious crime.
Jake
Clyde
The DA puts Jake & Clyde in separate rooms and makes each the following
offer:
Keep your mouth shut and you both get one year in jail
If you rat on your partner, you get off free while your partner does 8
years
If you both rat, you each get 4 years.
Jake is choosing rows
Clyde is choosing columns
Clyde
Jake
Confess Don’t
Confess
Confess -4 -4
0 -8
Don’t
Confess
-8
0
-1
-1
Suppose that Jake believes that Clyde will confess. What is
Jake’s best response?
If Clyde confesses, then
Jake’s best strategy is
also to confess
Jake
Clyde
Confess Don’t
Confess
Confess -4 -4
0 -8
Don’t
Confess
-8
0
-1
-1
Suppose that Jake believes that Clyde will not confess. What is
Jake’s best response?
If Clyde doesn’t
confesses, then Jake’s
best strategy is still to
confess
Jake
Clyde
Confess Don’t
Confess
Confess -4 -4
0 -8
Don’t
Confess
-8
0
-1
-1
Dominant Strategies
Jake’s optimal strategy
REGARDLESS OF CLYDE’S
DECISION is to confess.
Therefore, confess is a
dominant strategy for Jake
Clyde
Jake
Note that Clyde’s
dominant strategy is
also to confess
Confess Don’t
Confess
Confess -4 -4
0 -8
Don’t
Confess
-8
0
-1
-1
Nash Equilibrium
The Nash equilibrium is the outcome (or
set of outcomes) where each player is
following his/her best response to their
opponent’s moves
Jake
Here, the Nash equilibrium is
both Jake and Clyde
confessing
Clyde
Confess Don’t
Confess
Confess -4 -4
0 -8
Don’t
Confess
-8
0
-1
-1
Repeated Games
Jake
Clyde
The previous example was a
“one shot” game. Would it
matter if the game were
played over and over?
Suppose that Jake and Clyde were habitual (and very lousy)
thieves. After their stay in prison, they immediately commit the
same crime and get arrested. Is it possible for them to learn to
cooperate?
0
1
2
Play
PD Game
Play
PD Game
Play
PD Game
Time
3
Play
PD Game
4
Play
PD Game
5
Play
PD Game
Repeated Games
Jake
Clyde
We can use backward induction to solve this.
0
1
2
Play
PD Game
Play
PD Game
Play
PD Game
Time
Confess
Confess
Confess
Confess
Confess
Confess
3
Play
PD Game
Confess
Confess
4
5
Play
PD Game
Play
PD Game
Confess
Confess
Confess
Confess
Similar arguments take us back to period 0
However, once the equilibrium for period 5 is known, there
is no advantage to cooperating in period 4
At time 5 (the last period), this is a one shot game (there is no future).
Therefore, we know the equilibrium is for both to confess.
Continuous Choice Games – Cournot Competition
p
There are two firms in an industry –
both facing an aggregate (inverse)
demand curve given by
D
Q
P  A  BQ
Aggregate
Production
Q  q1  q2
Both firms have constant marginal costs equal to $C
From firm one’s perspective, the demand curve is given by
P  A  Bq1  q2    A  Bq2   Bq1
Treated as a constant by Firm One
Solving Firm One’s Profit Maximization…
MR   A  Bq2   2Bq1  c
q1

A  Bq 2   c

2B
In Game Theory Lingo, this is Firm One’s Best Response
Function To Firm 2
 Ac  1
q1  
  q2
 2B  2
q2
 Ac


 B 
Note that this is the optimal
output for a monopolist!
 Ac


 2B 
q1
Further, if Firm two produces
 Ac


 B 
q2
 Ac


 B 
It drives price down to MC
P  A  BQ
 Ac 
P  A  B
c
 B 
 Ac


 2B 
q1
The game is symmetric with respect to Firm two…
 Ac  1
q1  
  q2
 2B  2
q2
 Ac


 B 
 Ac  1
q2  
  q1
 2B  2
Firm 1
 Ac


 2B 
Firm 2
 Ac


 2B 
 Ac


 B 
q1
1 Ac 
q1  q  

3 B 
*
2 Ac 
Q  q1  q  

3 B 
*
*
2
q2
*
2
1  Ac  2 Ac   Ac 

 


2 B  3 B   B 
Firm 1
Competitive
Output
Monopoly
Output
q 2*
There exists a unique Nash
equilibrium
Firm 2
*
q1
q1
A numerical example…
Suppose that the market demand for computer chips (Q is in millions)
is given by
P  120  20Q
Intel and Cyrix are both competing in the market and have a
marginal cost of $20.
1  120  20  5
q q  
   1.67 M
3  20  3
*
I
*
C
P  120  20(3.33)  $53.33
Had this market been serviced instead by a monopoly,
P  120  20Q
MC  $20
Q*  2.5M
P  120  20(2.5)  $70
dQ P
1  70 

 
  1.4
dP Q
20  2.5 
MC
p
 1
1  
 
$20
$70 
1 

1 

 1 .4 
With competing duopolies
P  120  20q2   20q1  86.6  20q1
MC  $20
Q*  1.67 M
P  86.6  20(1.67)  $53.33
dQ P
1  53.33 

 
  1.6
dP Qi
20  1.67 
MC
p
 1
1  
 
$20
$53.33 
1 

1 

 1.6 
One more point…
Monopoly
Duopoly
Q*  2.5M
Q*  1.67 M
P  $70
P  $53.33
  ($70  $20)2.5  $125
  ($53  20)1.67  $55
If both firms agreed to produce 1.25M chips (half the monopoly output),
they could split the monopoly profits ($62.5 apiece). Why don’t these
firms collude?
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  A  BQ
Q
Just as before, we have an industry
demand curve and two competing
duopolies – both with marginal cost
equal to c.
Cournot Case
Bertrand Case
Q  a  bP
P  A  BQ
p
 A  Bq2 
p1
p2
D
q1
D
q1
Price competition creates a discontinuity in each firm’s demand curve –
this, in turn creates a discontinuity in profits
if p1  p2
0



 a  bp1 
 1  p1 , p2   ( p1  c)
 if p1  p2
 2 


 ( p  c)( a  bp ) 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  c
p1  p2  
Case #3: Firm 2 sets a price below marginal cost
c  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?
Bertrand Equilibrium: It only takes two firm’s in the
market to drive prices to marginal cost and profits to
zero!
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