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 (Positive Markup)
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 significant 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)
Anheuser-Busch: 49%
Miller/Coors: 29%
Crown Imports: 5%
Heineken USA: 4%
Pabst: 3%
Music Recording (2005)
Universal/Polygram: 31%
Sony: 26%
Warner: 15%
Warner: 10%
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!
Strategy Matters!!!!!
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
“Winston tastes good like a
cigarette should!”
“Us Tareyton smokers would
rather fight than switch!”
Advertise
Don’t
Advertise
Advertise
10 10
30
Don’t
Advertise
5
20 20
30
5
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!
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
$20 $20
$10
$40
Cheat
$40
$15
$15
$10
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
$20 $20
$10
$40
Cheat
$40
$15
$15
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
$10
2
Make Strategic
Decision
3
Make Strategic
Decision
4
Make Strategic
Decision
5
Make Strategic
Decision
Cooperate
“I plan on cooperating…if you cooperate
today, I will cooperate tomorrow, but if
you cheat today, I will cheat forever!”
Jake
Cooperate:
$20
Cheat
Cooperate
$20 $20
$10
$40
Cheat
$40
$15
$15
$10
$20
$20
$20
$20
$20
0
1
2
3
4
5
Make Strategic
Decision
Make Strategic
Decision
Clyde
Time
Cheat:
$40
Cooperate: $120
Cheat: $115
$15
Make Strategic
Decision
$15
Make Strategic
Decision
$15
Make Strategic
Decision
Make Strategic
Decision
$15
$15
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
Make Strategic
Decision
Clyde
4
5
Make Strategic
Decision
Make Strategic
Decision
Cooperate
Regardless of what took place the
first four time periods, what will
happen in period 5?
Cheat
Cooperate
$20 $20
$10
$40
Cheat
$40
$15
$15
$10
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
4
Make Strategic
Decision
Clyde
5
Make Strategic
Decision
Make Strategic
Decision
Cheat
Cooperate
Given what
happens in period
5, what should
happen in period 4?
Cheat
Cooperate
$20 $20
$10
$40
Cheat
$40
$15
$15
$10
What should
Clyde do here?
We need to use backward
induction to solve this.
0
1
Make Strategic
Decision
Make Strategic
Decision
Time
2
Cheat
Cooperate
Make Strategic
Decision
Cheat
3
Make Strategic
Decision
Cheat
Cheat
Cooperate
$20 $20
$10
$40
Cheat
$40
$15
$15
$10
Jake
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
The Stag Hunt: Two individuals are out on a hunt. Each must make a decision on
what to hunt without knowledge of the other individual’s choice
Only one hunter is required to
catch a rabbit – a small, sure
reward
Two hunters are required to take
down a stag – a bigger but riskier
reward
Stag
What’s the equilibrium
here?
Rabbit
Stag
4
4
0
1
Rabbit
1
0
1
1
The Stag Hunt: Two individuals are out on a hunt. Each must make a decision on
what to hunt without knowledge of the other individual’s choice
If both hunt the stag, neither
has an incentive to deviate –
an equilibrium!
Stag
Rabbit
Stag
4
4
0
1
Rabbit
1
0
1
1
If both hunt the rabbit, neither
has an incentive to deviate –
an equilibrium!
A quick detour: Expected Value
Suppose that I offer you a
lottery ticket: This ticket has a
2/3 chance of winning $100 and
a 1/3 chance of losing $100.
How much is this ticket worth to
you?
Suppose you played this ticket 6 times:
Attempt
Outcome
1
$100
2
$100
3
-$100
4
$100
5
-$100
6
$100
Total Winnings: $200
Attempts: 6
Average Winnings: $200/6 = $33.33
A quick detour: Expected Value
Given a set of probabilities,
Expected Value measures the
average outcome
Expected Value = A weighted average of the possible outcomes where the
weights are the probabilities assigned to each outcome
Suppose that I offer you a
lottery ticket: This ticket has a
2/3 chance of winning $100 and
a 1/3 chance of losing $100.
How much is this ticket worth to
you?
2
1
EV   $100    $100   $33.33
3
 3
Suppose that you believed that
your fellow hunter was equally
likely to hunt the stag or the rabbit
what would you do?
50%
50%
Stag
Rabbit
Stag
4
4
0
1
Rabbit
1
0
1
1
If you hunt the rabbit: You are guaranteed a
reward of 1 with certainty
If you hunt the stag: 50% of the time you get 4,
50% of the time you get 0
EV  .504  .500  2
In this example, hunting the stag is reward dominant (better average
payout), while hunting the rabbit is risk dominant (lower risk)
What if we change the odds…?
10%
90%
Stag
Rabbit
Stag
4
4
0
1
Rabbit
1
0
1
1
If you hunt the rabbit: You are guaranteed a
reward of 1 with certainty
If you hunt the stag: 10% of the time you get 2,
90% of the time you get 0
EV  .104  .900  .4
Now, hunting the rabbit is both reward dominant and risk dominant!!
Choosing the stag would never be a good idea here.
Let’s find the odds that make the
stag and rabbit equally attractive on
average…
X%
Y%
Stag
Rabbit
Stag
4
4
0
1
Rabbit
1
0
1
1
If you hunt the rabbit: You are guaranteed a
reward of 1 with certainty
If you hunt the stag:
EV   X 4  Y 0
For them to be
equal on average:
 X 4  Y 0  1
4X  1
X  .25
X = 25%, Y = 75%
Therefore, in this example,
you will only hunt the stag if
your fellow hunter hunts the
stag at least 25% of the
time.
Similarly, your fellow hunter
will only hunt the stag if you
hunt the stag at least 25% of
the time.
25%
75%
Stag
25%
Stag
4
6.25%
Rabbit
75%
4
Rabbit
1
0
18.75%
0
1
18.75%
1
1
56.25%
Therefore, in this case, the
stag hunt has three possible
equilibria:
50%
50%
Stag
Rabbit
Stag
4
4
0
1
Rabbit
1
0
1
1
Equilibrium #1: Both players always
hunt the stag
Equilibrium #2: Both players sometimes
hunt the stag (each player must hunt
the stag at least 25% of the time)
Equilibrium #3: Both players never hunt
the stag
Example: The Airline Price Wars
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
p
$500
$220
American
180
What will the equilibrium
be?
Q
P = $500
P = $220
P = $500
$9,000
$9,000
$3,600
$0
P = $220
$0
$3,600
$1,800
$1,800
Delta
60
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 is just like the stag
hunt – it 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: A Stag Hunt!
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%)
Lets take the game we started out with…what are the strategies?
Player 1
Player 2
Rock
Paper
Scissors
Rock
0
0
-1
1
1
-1
Paper
1
-1
0
0
-1
1
Scissors
-1
1
1
-1
0
0
Ever Cheat on your taxes?
In this game you get to
decide whether or not to
cheat on your taxes while
the IRS decides whether or
not to audit you
Cheat
Don’t
Cheat
What is the
equilibrium to this
game?
Don’t
Audit
Audit
5 -5 -25 5
0
0
-1
-1
If the IRS never audited, your best strategy is to cheat (this would only make
sense for the IRS if you never cheated)
If the IRS always audited, your best strategy is to never cheat (this would
only make sense for the IRS if you always cheated)
There is no pure strategy
equilibrium (i.e. there are no
certain strategies)!
Cheat
Don’t
Cheat
Don’t
Audit
Audit
5 -5 -25 5
0
0
-1
-1
Cheating on your taxes!
Suppose that the IRS Audits 25% of all returns. What should you do?
Cheat: EV  .755  .25 25  2.5
Don’t Cheat: EV  .750  .251  .25
If the IRS audits
25% of all
returns, you are
better off not
cheating. But if
you never cheat,
they will never
audit, …
Cheat
Don’t
Cheat
Don’t
Audit
Audit
5 -5 -25 5
0
0
-1
-1
The only way this game can work is for you to cheat sometime, but not all the
time. That can only happen if you are indifferent between the two!
Suppose the government audits with probability p A
Doesn’t audit with probability pDA
Cheat:
EV   pDA 5   pA  25
Don’t Cheat:
EV   pDA 0  PA 1
If you are indifferent…
5 pDA  25 p A   p A
5 pDA  24 p A
5
pA 
pDA
24
p A  pDA  1
Don’t Audit
Audit
Cheat
5
-5
-25
Don’t Cheat
0
0
-1
5
pDA  pDA  1
24
29
pDA  1
24
24
pDA 
(83%)
29
pA 
5
-1
5
(17%)
29
We also need for the government to audit sometime, but not all the time. For
this to be the case, they have to be indifferent!
Suppose you cheat with probability pC
Don’t cheat with probability
Audit:
pDC
EV   pDC  1   pC 5
Don’t Audit:
EV   pDC 0  PC  5
If they are indifferent…
5 pC  pDC  5 pC
10 pC  pDC
1
pC 
pDC
10
pC  pDC  1
Don’t Audit
Audit
Cheat
5
-5
-25
Don’t Cheat
0
0
-1
pA 
1
(9%)
11
1
p DC  p DC  1
10
11
p DC  1
10
10
p DC 
(91%)
11
5
-1
Now we have an equilibrium for this game that is sustainable!
The government audits with probability p  17%
A
Doesn’t audit with probability p  83%
DA
Suppose you cheat with probability pC  9%
Don’t cheat with probability pDC  91%
Don’t Audit
Cheat
5
-5
(7.5%)
We can find the odds of any
particular event happening….
You Cheat and get audited:
pC  p A   .09.17  .0153
Don’t Cheat
0
0
(75%)
(1.5%)
Audit
-25
5
(1.5%)
-1
-1
(15%)
In the Movie Air Force One,
Terrorists hijack Air Force
One and take the president
hostage. Can we write this
as a game? (Terrorists
payouts on left)
Terrorists
President
(1, -.5)
(0, 1)
In the third stage, the best
response is to kill the hostages
Terrorists
Given the terrorist response, it is
optimal for the president to
negotiate in stage 2
(-.5, -1)
(-1, 1)
Given Stage two, it is optimal
for the terrorists to take
hostages
Terrorists
The equilibrium is always (Take
Hostages/Negotiate). How could we
change this outcome?
President
(1, -.5)
(0, 1)
Suppose that a constitutional
amendment is passed ruling out
hostage negotiation (a commitment
device)
Terrorists
Without the possibility of
negotiation, the new equilibrium
becomes (No Hostages)
(-.5, -1)
(-1, 1)
A bargaining
example…How do
you divide $20?
Player A
Offer
Player B
Accept
Day 1
Reject
Player B
Two players have $20 to
divide up between them.
On day one, Player A
makes an offer, on day two
player B makes a
counteroffer, and on day
three player A gets to make
a final offer. If no
agreement has been made
after three days, both
players get $0.
Offer
Player A
Accept
Day 2
Reject
Player A
Offer
Player B
Accept
Day 3
Reject
(0,0)
Player A
Offer
Player B
Accept
Reject
Player A knows
Day 1 what happens in
day 2 and wants to
avoid that!
Player A: $19.99
Player B: $.01
Player B knows
what happens in
Day 2 day 3 and wants to
avoid that!
Player A: $19.99
Player B: $.01
Player B
Offer
Player A
Accept
Reject
Player A
Offer
Player B
Accept
Reject
(0,0)
If day 3 arrives,
Day 3 player B should
accept any offer –
a rejection pays
out $0!
Player A: $19.99
Player B: $.01
Player A
Lets consider a
variation…
Offer
Player B
The Shrinking Pie Game:
Negotiations are costly. After
each round, the pot gets
reduced by 50%:
Accept
Day 1
$20
Reject
Player B
Offer
Player A
Accept
Day 2
$10
Reject
Player A
Offer
Player B
Accept
Day 3
Reject
(0,0)
$5
Player A
If player B rejects,
she gets $5
Day 1 tomorrow. She will
accept anything
$20
better than $5
Offer
Player B
Accept
Reject
Player A: $5.01
Player B: $14.99
Player B
Offer
Player A
Accept
Day 2
Reject
$10
If player A rejects,
she gets $4.99 in
one year. She will
accept anything
better than $4.99
Player A: $5.00
Player B: $5.00
Player A
Offer
Player B
Accept
Reject
(0,0)
If day 3 arrives,
Day 3 player B should
accept any offer –
a rejection pays
$5
out $0!
Player A: $4.99
Player B: $.01
Did someone say Batman?
Back to pricing…
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?
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
P  120  20Q
Let’s figure out the strategies…
TR
Q1
Suppose that you are firm 1. You know that firm
#2 has set a production level of 1
Q2
Q1
Q
P
TR
MR
1
0
1
100
0
1
.25
1.25
95
23.75
95
1
.5
1.5
90
45
85
1
.75
1.75
85
63.75
75
1
1
2
80
80
65
1
1.25
2.25
75
93.75
55
1
1.5
2.5
70
105
45
1
1.75
2.75
65
113.75
35
1
2.00
3
60
120
25
1
2.25
3.25
55
123.75
15
P  120  201  Q1
Recall, firm 2 has set its
production at 1
P  100  20Q1
P
$100
$20
MC
D
MR
2
Q1
P  120  20Q
Let’s figure out the strategies…
TR
Q1
Now, Suppose that you are firm 1. You know that
firm #2 has set a production level of 2
Q2
Q1
Q
P
TR
MR
2
0
2
80
0
2
.25
2.25
75
18.75
75
2
.5
2.5
70
35
65
2
.75
2.75
65
48.75
55
2
1
2
60
60
45
2
1.25
2.25
55
68.75
35
2
1.5
2.5
50
75
25
2
1.75
2.75
45
78.75
15
2
2.00
2
40
75
5
2
2.25
2.25
35
68.75
-5
An increase in production by firm 1 shifts
the demand curve faced by firm #1 down
which causes production by firm 1 to drop
P  120  202  Q1
P  80  20Q1
P
$100
$80
$20
MC
D
MR
1.5
2
Q1
Whenever firm #2 increases its production, firm 1’s best response is to
reduce its production
In Game Theory Lingo, this is Firm One’s Best
Response Function To Firm 2
q2
q2  5
q1  0
Firm 2
chooses 1.5
0
Firm 1
chooses
1.75
q2  0
q1  2.5
Q2
Q1
0
2.5
.25
2.375
.50
2.25
.75
2.125
1
2
1.25
1.875
1.5
1.75
1.75
1.625
2
1.5
2.25
2.375
2.5
1.25
q1
The game is symmetric with respect to Firm two…
Q1
Q2
0
2.5
.25
2.375
.50
2.25
.75
2.125
1
2
1.25
1.875
q1  0
1.5
1.75
q2  2.5
1.75
1.625
2
1.5
2.25
2.375
2.5
1.25
q2
Firm 2
responds
with a
production
target of
1.675
q1  5
q2  0
Firm 1 chooses a
production target of
1.75
q1
Eventually, these two firms converge on production levels such that
neither firm has an incentive to change
q1*  q2*  1.67M
q2
P  120  20(3.33)  $53.33
Firm 1
 1  53.331.67   201.67   $55.66
 2  53.331.67   201.67   $55.66
HHI  50 2  50 2  5000
q  1.67
*
2
Firm 2
q1*  1.67
q1
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
Suppose Firm 2’s marginal costs increase to $30
P
$20
MC
D
MR
1.67
Firm 2’s production drops…
Q1
Firm 2’s production drops…
P
$100
$80
$20
MC
D
MR
1.67
Q1
Firm 1’s best response is to increase it’s production
Firm #2 loses market share to Firm #1
q2
Q  1.33  1.83  3.16
P  120  203.16   $56.8
 1  56.81.83  201.83  67.34
Firm 1
 2  56.81.33  301.33  35.64
HHI  42 2  582  5128
LI  .64
q2  1.33
42%
Firm 2
q  1.83
*
1
q1
58%
Firm 2’s market share drops
Now, consider another example. Both firms have a constant marginal cost of $20
Two manufacturers
choose a Price
P1
Q  6  .05 P
Potential
customers observe
the prices offered
and choose how
much/from whom
to buy
Two manufacturers
earn profits based
off the market price
Profit = ??
Profit = ??
P2
With Identical products, consumers choose the
cheapest!
Firm level demand curves look very different when we are competing in price.
Firm Level Demand
Industry Demand
Q  6  .5 P
p
p1
p2
D
q1
If you are
underpriced, you lose
the whole market
At equal
prices, you
split the
market
q
D
q0
6  .05 P
2
q1
If you are
the low
price you
capture the
whole
q  6  .05P
market
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?