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

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?

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

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

A limit pricing model

ACe

MCe

$/unit

Quantity

These are the cost curvesfor the potential entrant

These are the cost curvesfor the potential entrant

D(P) = Market DemandAssume that the

incumbent commitsto output Q1

Assume that theincumbent commits

to output Q1

Q1

Then the entrant’s residual demand is

R1 = D(P) - Q1

Then the entrant’s residual demand is

R1 = D(P) - Q1

R1

With the residual demand R1, the entrant can operate profitably.

Entry is not deterred by the incumbent choosing Q1.

With the residual demand R1, the entrant can operate profitably.

Entry is not deterred by the incumbent choosing Q1.

Assume instead that the incumbent

commits to output Qd

Assume instead that the incumbent

commits to output Qd

The entrant’s residualdemand is

Re = D(P) - Qd

The entrant’s residualdemand is

Re = D(P) - Qd

Qd

Re

MRe

qe

Pe

Then the entrant’s marginal revenue is MRe

Then the entrant’s marginal revenue is MRe

The entrant equatesmarginal revenuewith marginal cost

The entrant equatesmarginal revenuewith marginal cost

At price Pe entry isunprofitable

At price Pe entry isunprofitable

Qd

Pd

By committing to outputQd the incumbent detersentry. Market price Pd

is the limit price

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

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

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 entrant 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)

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

The Dixit model 3

• The incumbent’s best response function has a break in it at K1

q2

q1

L’

L

N’

N

K1

• The entrant’s best response function has a break where sunk costs are not covered

R’

R• Equilibrium depends upon these two breaks

The Dixit model 4• Consider the possibilities q2

q1

L’

L

N’

N

R’

R

T

VT2

T1

V2

V1

• 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

The Dixit model 5• Now suppose that firm 2

does not enter

q2

q1

L’

L

N’

N

R’

R

T

VT2

T1

V2

V1

• 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

M2

S• M1 is actually the Stackelberg output level for firm 1– firm 1 as market leader will

never choose output and capacity less than M1

The Dixit model 6• Suppose that the break in the

entrant’s best response function lies at BL in R’T

q2

q1

L’

L

N’

N

R’

R

T

VT2

T1

V2

V1M1

M2

S

BL

• Incumbent chooses capacity M1 and entry is deterred

• Suppose that the break in the entrant’s best response function lies at BS in TS BS

• Incumbent chooses capacity M1 and entry is deterred

• Suppose that the break in the entrant’s best response function lies at BL in VR

• Incumbent chooses capacity M1 and entry is accommodated

BL

The Dixit model 7• Now suppose that the break

in the entrant’s best response function lies at B* in SV

q2

q1

L’

L

N’

N

R’

R

T

VT2

T1

V2

V1M1

M2

S

• Incumbent can choose to install capacity M! and share the market

• Or install capacity B! and maintain monopoly in the market

B1

• Choice depends upon relative profitability

– If B* is “close to” S then use capacity to deter entry– If B* is “close to” V then accommodate entry as Stackelberg leader

B*

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.

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

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:

Preemption and the persistence of monopoly 2• A market with an incumbent

– current profit M

– 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 2M minus cost of capacity

• With threat of entry may need to install capacity early

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 + 2C/(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 = 2C/(1 – R) – RF in

present value terms

– suppose e1 < e

2 which implies (1 + r)C < rF

– entrant will enter in the second period

Preemption and the persistence of monopoly 4• What about the incumbent?

– do nothing in period 1• entry takes place in period 2• earns 2C/(1 – R)

– install additional capacity in period 1• entry deterred• earns 2M/(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

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

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%