Limit Pricing and Entry Deterrence
Chapter 12: Limit Pricing and Entry
Deterrence
1
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
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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
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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
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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
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Then the entrant’s
residual demand is
R1 = D(P)
- Q1
$/unit
Pd
Pe
A limit pricing model
These are the cost curves
for
potential entrant
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With the residual demand R1, Qd the incumbent deters
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e entry is
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entrant’s residual
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Re
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Qd
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Chapter 12: Limit Pricing and Entry
Deterrence
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Limit pricing
• 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
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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
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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
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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
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The Dixit model 3
• The incumbent’s best
response function has a
break in it at K1
• The entrant’s best
response function has a
break where sunk costs are
not covered
• Equilibrium depends upon
these two breaks
q2
L’
N’
R’
Chapter 12: Limit Pricing and Entry
Deterrence
R
N
K1
L
q1
11
The Dixit model 4
q2
• 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
• So capacity choice lies
between T1 and V1
L’
N’
R’
T2
T
V
V2
R
N
T1
Chapter 12: Limit Pricing and Entry
Deterrence
V1 L
q1
12
The Dixit model 5
q2
• 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
L’
N’
R’
T2
M2
V2
T
S
V
R
N
T1
M1
V1 L
q1
– firm 1 as market leader will
never choose output and
capacity less than M1
Chapter 12: Limit Pricing and Entry
Deterrence
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The Dixit model 6
• 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
T2
M
2
• Incumbent chooses capacity
V2
M1 and entry is deterred
q2
L’
N’
R’ BL
T B
S
S
V
BL
N
T1
M1
V1 L
R
q1
• 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
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The Dixit model 7
• 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
T2
M
2
market
V2
• Choice depends upon relative
profitability
q2
L’
N’
R’
T
S
B* V
N
T1
M1 B1 V1 L
R
q1
– 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
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Capacity expansion and entry deterrence 2
• An example:
–
–
–
–
–
–
P = 120 - Q = 120 - (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
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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
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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
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Preemption and the persistence of monopoly 2
• A simple 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 2pM minus cost of capacity
• With threat of entry may need to install capacity early
Chapter 12: Limit Pricing and Entry
Deterrence
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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 pe1 = pC + 2pC/(1 – R) - F
• R is the discount factor = 1/(1+r) where r is the discount rate
– entry in period 2 gives the entrant pe2 = 2pC/(1 – R) – RF in present
value terms
– suppose pe1 < pe2 which implies (1 + r)pC < r.F
– entrant will enter in the second period
Chapter 12: Limit Pricing and Entry
Deterrence
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Preemption and the persistence of monopoly 4
• What about the incumbent?
– do nothing in period 1
• entry takes place in period 2
• earns 2pC/(1 – R)
– install additional capacity in period 1
• entry deterred
• earns 2pM/(1 – R) – F
– install capacity early provided that 2(pM - pC)/(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
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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
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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
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