Another trick that may help prevent entry:
Raising the costs of all firms in the industry (pp.488-491)
You are a monopolist, earning $10 (million) in profit.
If another firm enters, then each of you would earn $3.
You can convince the government to require pollutioncontrol devices that would raise everyone’s costs by $4.
Let’s represent this as a sequential game, with the
government moving first:
Firm 1
Lobby for devices
Not
Firm 2
Enter
-1, -1
Firm 2
Do Not Enter
6, 0
Enter
3, 3
Do Not Enter
10, 0
Limit pricing
You are the monopolistic incumbent:
What quantity is best to produce?
- Find MR = MC
- Determine quantity,
price, and profit
MC
PINC
ATC
Demand
Q
QINC
MR
Limit pricing
You are the incumbent:
… then this is the additional quantity that
can be sold at any given price.
It is called “residual demand”
MC
ATC
P
Q
If this is the quantity produced by the incumbent…
Limit pricing
You are the incumbent:
Suppose there is a firm with the
same cost structure as ours.
Can that firm enter “our” market
profitably?
MC
Yes it can!
P > ATC
ATC
Demand
Q
This is a problem: if another company enters, our
profit would decrease substantially.
Furthermore, if (in the worst case scenario) the
new firm starts a price war, our profit may go all
the way down to zero.
How can we prevent this from happening?
The competitor will not enter if entry is unprofitable!
Instead of producing the profit-maximizing quantity,
you need to “flood” the market by lowering the price
and increasing the quantity produced so that the
residual demand is pushed far enough to the left to
make entry unprofitable.
Limit pricing
You are the incumbent:
MC
ATC
P
This is where you need
the residual demand to be
Q
Q
Therefore these are your
safe P, Q, and profits
Instead of deviating from the profit-maximizing
quantity of output, can’t you simply make a threat to
potential entrants that, in case they enter, you
increase your output, lower your price and thus make
the entrant lose money?
Limit pricing as illustrated above
Incumbent
Profit-max price
Lower price (limit pricing)
Entrant
Entrant
enter
no
3, 3
20, 0
enter
- 1, -1
no
6, 0
First entry is for the player moving first (the incumbent)
Lowering price in response to entry
Entrant
enter
no
Incumbent
Incumbent
High P
Low P
High P
3, 3
- 1, - 1
0, 20
First entry is for the player moving first (the entrant)
Low P
0, 6
How can a firm deter entry? – A summary
•Pay for exclusive rights;
•Make new entry unprofitable:
•strategic lobbying for new laws;
•limit pricing;
•reduce the degree of substitutability between the two
products:
•advertising;
•reputation;
•filling all niches;
•“burn bridges” (make an irreversible credible
commitment):
•build a large plant;
•invest in a technology.
Non-credible threats do not work!!!
Infinitely repeated games
The concept of present value (see pp.14-18):
Profit today is more valuable than profit one year from today.
The present value of the future profit is
Profit
PV = ---------- ,
(1+i)
where i is the discounting factor, usually set equal to the
interest rate.
A firm that is believed to exist and earn profits infinitely into
the future has the present value of
PV = π 0 +
π1
(1 + i )
+
π2
(1 + i )
2
+
π3
(1 + i )
3
+ ⋅⋅⋅
(Such an expression is called an infinite series.)
A couple of useful facts about infinite series:
If the profits, π, are the same in each period and we
start counting with the present period, then
π
π
π
π
(1 + i )π
+
+
+ ⋅⋅⋅ =
=π +
PV = π +
2
3
(1 + i ) (1 + i )
(1 + i )
i
i
If the first period in the series is “a year from now”,
then
PV =
π
(1 + i )
+
π
(1 + i )
2
+
π
(1 + i )
3
+ ⋅⋅⋅ =
π
i
Airline pricing game, revisited
Firm 2
Low price
High price
Low price
3, 3
8, 1
High price
1, 8
6, 6
Firm 1
What if this game is played repeatedly?
Firms use “trigger strategies” – strategies contingent on the
past play of a game (a certain action “triggers” a certain
response).
Suppose both firms are currently keeping their prices high.
An example of a trigger strategy:
“I will continue to play “HIGH” as long as you are playing
“HIGH”. Once you cheat by playing “LOW”, I will play
“LOW” in every period thereafter.”
If firm 1 continues to cooperate, its present value is
PVcoop = π +
π
(1 + i )
+
π
(1 + i )
2
+
π
(1 + i )
3
+ ⋅⋅⋅
Firms use “trigger strategies” – strategies contingent on the
past play of a game (a certain action “triggers” a certain
response).
Suppose both firms are currently keeping their prices high.
An example of a trigger strategy:
“I will continue to play “HIGH” as long as you are playing
“HIGH”. Once you cheat by playing “LOW”, I will play
“LOW” in every period thereafter.”
If firm 1 continues to cooperate, its present value is
PVcoop = 6 +
6
6
6
6
6
+
+
+
⋅
⋅
⋅
=
+
(1 + i ) (1 + i ) 2 (1 + i ) 3
i
If firm 1 cheats, its present value is
PVcheat
3
3
3
3
= 8+
+
+
+ ⋅⋅⋅ = 8 +
2
3
(1 + i ) (1 + i )
(1 + i )
i
Firm 1 will prefer to cooperate if
PVcoop > PVcheat
or
6
3
6+ > 8+
i
i
or
6i+6>8i+3
3>2i
i < 66.7%
If the rate of discounting is less
than 66.7%, then both firms
prefer to cooperate
Another example of a trigger strategy:
Quality choice by a firm.
The good can be purchased repeatedly.
Firm
Low quality High quality
Don’t buy
0; 0
0; - 10
- 10; 10
1; 1
Consumer
Buy
A trigger strategy by consumers that can support the
mutually beneficial outcome:
“I will buy your product as long as you produce high
quality. Once you produce low quality, I will never buy
your product again”