1. Limit Pricing and Entry Deterrence
Chapter 12: Limit Pricing and Entry Deterrence

2. Chapter 12: Limit Pricing and Entry Deterrence
Introduction
A firm that can restrict output to raise market price has market power
Microsoft (95% of operating systems) and Campbell’s (70% of tinned soup market) are giants in their industries
Have maintained their dominant position for many years
Why can’t existing rivals compete away the position of such firms?
Why aren’t new rivals lured by the profits?
Answer: firms with monopoly power may
eliminate existing rivals
prevent entry of new firms
These actions are predatory conduct if they are profitable only if rivals, in fact, exit
e.g., R&D to reduce costs is not predatory
Chapter 12: Limit Pricing and Entry Deterrence

3. Evolution of market structure
Evolution of markets depends on many factors
one is relationship between firm size and growth
Gibrat’s Law
begin with equal sized firms
each grows in each period by a rate drawn from a random distribution
this distribution has constant mean and variance over time
result is that firm size distribution approaches a log-normal distribution
Very mechanistic
no strategy for growth
Including strategic decision making affects distribution but not conclusion that firm sizes are unequal
What about the facts in the market place?
Chapter 12: Limit Pricing and Entry Deterrence

4. Monopoly power and market entry
Several stylized facts about entry
entry is common
entry is generally small-scale
so small-scale entry is relatively easy
survival rate is low: >60% exit within 5 years
entry is highly correlated with exit
not consistent with entry being caused by excess profits
“revolving door”
reflects repeated attempts to penetrate markets dominated by large firms
Not always easy to prove that this reflects predatory conduct
But we need to understand predation it if we are to find it
Chapter 12: Limit Pricing and Entry Deterrence

5. Predatory conduct and limit pricing
Predatory actions come in two broad forms
Limit pricing: prices so low that entry is deterred
Predatory pricing: prices so low that existing firms are driven out
Outcome of either action is the same—the monopolist retains control of the market
Legal action focuses on predatory pricing because this case has an identifiable victim
a firm that was in the market but that has left
Consider first a model of limit pricing
Stackelberg leader chooses output first
entrant believes that the leader is committed to this output choice
entrant has decreasing costs over some initial level of output
Chapter 12: Limit Pricing and Entry Deterrence

6. A limit pricing model By committing to output Qd the incumbent deters
entry. Market price Pd
is the limit price
A limit pricing model
Then the entrant’s residual demand is
R1 = D(P) - Q1
These are the cost curves
for the potential entrant
With the residual demand R1, the entrant can operate profitably. Entry is not deterred by the
incumbent choosing Q1.
$/unit
Then the entrant’s marginal revenue is MRe R1
At price Pe entry is
unprofitable
The entrant’s residual
demand is
Re = D(P) - Qd
The entrant equates
marginal revenue
with marginal cost
MCe Pd
Assume instead that the incumbent commits to output Qd
ACe
Assume that the
incumbent commits
to output Q1 Pe
D(P) = Market Demand Re
MRe
Quantity qe Qd Q1 Qd
Chapter 12: Limit Pricing and Entry Deterrence

7. Chapter 12: Limit Pricing and Entry Deterrence
Committing to output Qd may be aimed either at eliminating an existing rival or driving out a potential entrant.
Either way, several questions arise:
Is limit pricing more profitable than other strategies?
Is the output commitment credible?
If output is costly to adjust then commitment is possible
why should this property hold?
could be claimed to be ad hoc to support the theory
even if it holds, is monopoly at output Qd better than Cournot?
may not be if the entrant’s costs are low enough
Credibility may relate output to capacity
Chapter 12: Limit Pricing and Entry Deterrence

8. Capacity expansion and entry deterrence
For predation to be successful and rational
the incumbent must convince the entrant that the market after the entrant comes in will not be profitable one
How can the incumbent credibly make this threat?
One possible mechanism
install capacity in advance of production
installed capacity is a commitment to a minimum level of output
the lead firm can manipulate entrants through capacity choice
the lead firm may be able to deter entry through its capacity choice
but is this credible?
capacity must be costly to install and should be irreversible
Chapter 12: Limit Pricing and Entry Deterrence

9. Chapter 12: Limit Pricing and Entry Deterrence
The Dixit model
Consider a two-stage game
incumbent in period 1 installs capacity
capacity K1 costs r.K1 to install
in second period incumbent can produce up to K1 at unit cost w
capacity can be expanded in period 2 at additional cost r per unit
capacity cannot be reduced in period 2
potential entrant in period 2 observes incumbent’s capacity choice
to enter and produce incumbent needs capacity K2 which costs r.K2
unit cost of production is w
note: entrant will never install unused capacity
if entry takes place firms play a Cournot game in the second period
Market demand: P = A – B(q1 + q2)
Chapter 12: Limit Pricing and Entry Deterrence

10. Chapter 12: Limit Pricing and Entry Deterrence
The Dixit model 2
Costs for the incumbent are:
C1 = F1 + w.q1 + r.K1 for q1 < K1; marginal cost w
C1 = F1 + (w + r)q1 for q1 > K1; marginal cost w + r
Costs for the entrant are:
C2 = F2 + (w + r)q2 ; marginal cost w + r
Standard Cournot analysis gives the best response functions:
q*1 = (A – w)/2B – q2/2 when q1 < K1
q*1 = (A – w – r)/2B – q2/2 when q1 > K1
q*2 = (A – w – r)/2B – q1/2 provided that q*2 > 0
for the entrant to enter it must expect to cover the sunk costs F2
this implies a lower limit on the output that the entrant must make
Chapter 12: Limit Pricing and Entry Deterrence

11. Chapter 12: Limit Pricing and Entry Deterrence
The Dixit model 3 q2
The incumbent’s best response function has a break in it at K1 L’
The entrant’s best response function has a break where sunk costs are not covered N’ R’ R
Equilibrium depends upon these two breaks N L q1 K1
Chapter 12: Limit Pricing and Entry Deterrence

12. Chapter 12: Limit Pricing and Entry Deterrence
The Dixit model 4 q2 q1 L’ L N’ N R’ R
Consider the possibilities
Suppose that firm 2 enters
Equilibrium must lie between T and V
Where depends upon location of the break in R’R
Firm 1’s output is greater than T1 and smaller than V1 T T2 V
So capacity choice lies between T1 and V1 V2 T1 V1
Chapter 12: Limit Pricing and Entry Deterrence

13. Chapter 12: Limit Pricing and Entry Deterrence
The Dixit model 5 q2 q1 L’ L N’ N R’ R T V T2 T1 V2 V1
Now suppose that firm 2 does not enter
Must be that it cannot break even at output less than T2
Then firm 1 would want to choose capacity M1
this is the monopoly output with MC = w + r
M1 is actually the Stackelberg output level for firm 1
firm 1 as market leader will never choose output and capacity less than M1 S M2 M1
Chapter 12: Limit Pricing and Entry Deterrence

14. Chapter 12: Limit Pricing and Entry Deterrence
The Dixit model 6 q2 q1 L’ L N’ N R’ R T V T2 T1 V2 V1 M1 M2 S
Suppose that the break in the entrant’s best response function lies at BL in R’T
Incumbent chooses capacity M1 and entry is deterred
Suppose that the break in the entrant’s best response function lies at BS in TS BL BS
Incumbent chooses capacity M1 and entry is deterred BL
Suppose that the break in the entrant’s best response function lies at BL in VR
Incumbent chooses capacity M1 and entry is accommodated
Chapter 12: Limit Pricing and Entry Deterrence

15. Chapter 12: Limit Pricing and Entry Deterrence
The Dixit model 7 q2 q1 L’ L N’ N R’ R T V T2 T1 V2 V1 M1 M2 S
Now suppose that the break in the entrant’s best response function lies at B* in SV
Incumbent can choose to install capacity M! and share the market
Or install capacity B! and maintain monopoly in the market B*
Choice depends upon relative profitability B1
If B* is “close to” S then use capacity to deter entry
If B* is “close to” V then accommodate entry as Stackelberg leader
Chapter 12: Limit Pricing and Entry Deterrence

16. Capacity expansion and entry deterrence 2
An example:
P = Q = (q1 + q2)
marginal cost of production $60 for incumbent and entrant
cost of each unit of capacity is $30
firms also have fixed costs of F
incumbent chooses capacity K1 in stage 1
NOTE: incumbent will always produce at least K1 in production stage—otherwise it throws away revenue that could help cover the cost of installed capacity
entrant chooses capacity and output in stage 2
firms compete in quantities in stage 2.
Chapter 12: Limit Pricing and Entry Deterrence

17. Chapter 12: Limit Pricing and Entry Deterrence
Entry may not occur
entrant’s costs are too high
blockaded entry
not predatory
Entry may be accommodated
entrant’s costs are low
incumbent takes advantage of its being first in the market
but does not deter
Entry may be strategically deterred
strategic deterrence profitable for the incumbent
installs excess capacity as an entry-deterring strategy
uses a credible commitment
Chapter 12: Limit Pricing and Entry Deterrence

18. Preemption and the persistence of monopoly
A distinct but related issue is an incumbent investing early to prevent new entry
market may be a natural monopoly at current size
but expected to grow and attract entry
Now we have an issue of timing
It may be in the interests of an incumbent to preempt by
building new plants prior to a rival’s entry
adding new products prior to a rival’s entry
Related to another issue
entrant may race to innovate to preempt entry
A simple model:
Chapter 12: Limit Pricing and Entry Deterrence

19. Preemption and the persistence of monopoly 2
A market with an incumbent
current profit pM
market is expected to double in the next period and stay at the new size in perpetuity
to meet the new demand requires additional capacity at cost of F
the new capacity can be added:
In first period or in second period
By incumbent or by new entrant
With no threat of entry
incumbent installs new capacity at beginning of second period
profit is 2M minus cost of capacity
With threat of entry may need to install capacity early
Chapter 12: Limit Pricing and Entry Deterrence

20. Preemption and the persistence of monopoly 3
Consider the entrant choosing in period 1
suppose that competition is Cournot if entry occurs
entry in period 1 gives the entrant e1 = C + 2C/(1 – R) - F
R is the discount factor = 1/(1+r) where r is the discount rate
entry in period 2 gives the entrant e2 = 2C/(1 – R) – RF in present value terms
suppose e1 < e2 which implies (1 + r)C < rF
entrant will enter in the second period
Chapter 12: Limit Pricing and Entry Deterrence

21. Preemption and the persistence of monopoly 4
What about the incumbent?
do nothing in period 1
entry takes place in period 2
earns 2C/(1 – R)
install additional capacity in period 1
entry deterred
earns 2M/(1 – R) – F
install capacity early provided that 2(M - C)/(1 – R) > F
provided that present value of additional profit from protecting monopoly is greater than the fixed cost
Incumbent wants to maintain monopoly; entrant only shares in non-cooperative profits
Chapter 12: Limit Pricing and Entry Deterrence

22. Chapter 12: Limit Pricing and Entry Deterrence
Market preemption
Why does the incumbent have a stronger incentive to invest “early”?
the incumbent is protecting a valuable monopoly
the entrant is seeking a share of the market
so the incumbent’s incentive is stronger
willing to incur initial losses to maintain market control
Chapter 12: Limit Pricing and Entry Deterrence

23. Evidence on predatory expansion
Some anecdotal evidence
Alcoa
evidence that consistently expanded capacity in advance of demand
Safeway in Edmonton
evidence that it aggressively expanded store locations in response to potential entry
DuPont in titanium oxide
rapidly expanded capacity in response to to changes in rivals’ costs
market share grew from 34% to 46%
Chapter 12: Limit Pricing and Entry Deterrence