econs 425 - entry deterrence - washington state university · preventing entry in the typical entry...

EconS 425 - Entry Deterrence

Eric Dunaway

Washington State University

[email protected]

Industrial Organization

Eric Dunaway (WSU) EconS 425 Industrial Organization 1 / 44

Introduction

Now that we have characterized the oligopoly market structure, let�slook at how �rms with strong market power attempt to manipulatethat structure to their own ends.

Some of it is natural market behavior, some of it is very illegal.


Barriers to Entry

Let�s return to our four key assumptions of the perfectly competitivemarket.

Many buyers and sellers.Homogeneous products.Perfect Information.No Barriers to Entry and Exit.


Barriers to Entry

When we shifted from perfect competition to monopoly/oligopoly, werelaxed most of these assumptions.

Under monopoly, we have just one seller; or few sellers under oligopoly.Oligopolists usually want to add some heterogeneity to their productsin order to build market power.Monopoly assumes complete barriers to entry, while oligopoly assumesthat there are signi�cant barriers.


Barriers to Entry

Complete barriers to entry?

This is a convenient assumption to make, but unless the governmenthas granted a �rm a natural monopoly, this doesn�t happen in the realworld.Then why do we have this assumption in the �rst place?

A monopolist has many tools available to them to discourage entryinto their market.

As we observed in Stackelberg competition, �rst mover�s advantage isa very powerful tool that a monopolist can exploit to remain amonopolist.


Stylized Facts

In the real world, we see the frequent entry and exit of �rms intomarkets, even when the structure is not perfectly competitive.

For example, consider a market that undergoes a stochastic (random)process.

Suppose there are 256 �rms, each with a yearly revenue of $10 million.With probability 0.25, revenues decline by 15 percent. With probability0.25, revenues increase by 15 percent. And with probability 0.5,revenues stay the same.

Let�s see what happens to those �rms after a few years go by.


Stylized Facts

Year

1

2

3

$10

256


Stylized Facts

Year

1

2

3

$7.69 $10 $13.0

256

64 128 64


Stylized Facts

Year

1

2

3

$5.92 $7.69 $10 $13.0 $16.9

256

64 128 64

16 64 96 64 16


Stylized Facts

After just a few years, the largest �rms (in terms of revenue) are nowmaking almost three times as much as the smallest �rms.

If we let our random process continue, the disparity between the �rmsgets even worse.

In essence, a few �rms are able to claim large shares of the marketwhile many of the other �rms are pushed out.

As revenues decline, so do pro�ts, which induces exit from the market.


Stylized Facts

Several studies have looked at di¤erent markets and seen this processoccur. They have been able to conclude on four stylized facts:

Entry is common: Firms are always trying to enter markets when theythink they can carve out a niche for themselves.Entry is small scale: The Stackelberg e¤ect of large �rms holding on tomarket share is di¢ cult to overcome for newcomers.The survival rate is low: Most �rms that enter the market are forced toexit shortly after.Industries with high entry rates also have high exit rates: Volatilitytends to be a market thing, rather than entrepreneurial.


Stylized Facts

It�s interesting that the entry and exit rates of �rms are stronglycorrelated.

What�s happening here? Firms should have the ability to project theirlong term pro�ts and determine whether or not they should enter themarket.Perhaps it is truly a stochastic issue. An unforseen change in themarket (such as a signi�cant cost increase) could cause new �rms toleave.Or perhaps the incumbent �rm(s) creates a situation to encourage itsnew rival to exit the market?


Preventing Entry

Suppose a monopolist (�rm 1) were serving a market and wasthreatened by entry of a new �rm (�rm 2) into that market.

If the entrant were to enter the market, the incumbent monopolistwould become a Stackelberg leader, while the entrant would be aStackelberg follower.

The entrant must pay a sunk cost of F to enter the market. Supposemarket inverse demand were

p = a� b(q1 + q2)

and marginal costs were constant at c .


Preventing Entry

From before, we know that if the entrant to the market behaved as aStackelberg follower, their best response function to any output levelof the incumbent would be

q2(q1) =a� c2b

� q12

We can substitute this back into the entrant�s pro�t maximizationproblem to derive their pro�t level based on the incumbent�s outputlevel,

π2 = pq2 � cq2 � F

=

�a� b

�q1 +

a� c2b

� q12

�� c

� �a� c2b

� q12

�� F

=(a� c � bq1)2

4b� F


Preventing Entry

(a� c � bq1)24b

� F

Naturally, the entrant will only want to enter this market if theirpro�ts are positive. In fact, staying out of the market would be betterif

(a� c � bq1)24b

� F < 0

or, solving this expression for the sunk cost,

F >(a� c � bq1)2

4b


Preventing Entry

F >(a� c � bq1)2

4b

If the sunk cost of entry is high relative to the pro�t level of theentrant, they will not want to enter.

Look at what happens when I di¤erentiate the right side of thisexpression with respect to the incumbent�s output level,

∂π2∂q1

= �a� c � bq12

< 0

as the incumbent increases their quantity, the pro�t level (right-handside) of the entrant decreases.

In fact, the monopolist may want to give the entrant a little push outof the market in this case.


Preventing Entry

Would increasing the incumbent monopolist�s output level be in theirbest interest?

Suppose that if the monopolist produced the Stackelberg quantity, a�c2b(which is also the monopoly quantity) that the entrant would enter themarket. In this case, the monopolist�s pro�ts are the same as theStackelberg leader�s pro�ts we looked at before,

π1 =(a� c)28b

Now suppose that for some quantity greater than the monopolyquantity, the pro�ts for the entrants would become negative and causethem to not enter. This would let the incumbent remain as amonopolist.


Preventing Entry

If the incumbent can prevent entry, their pro�t level as a function oftheir own output level is

π1 = pq1 � cq1 = (a� c � bq1)q1

Suppose q̂1 is the minimum output level required to keep the entrantfor entering the market. The incumbent has to decide whether thispro�t level is more desirable than simply letting the entrant into themarket. Thus, if

(a� c � bq̂1)q̂1 >(a� c)28b

the monopolist would prefer to increase their own quantity to keepthe entrant out of the market.


Preventing Entry

π1

q1

(a c)2

8b

a c2b

(a c)2

4b


Preventing Entry

(a� c � bq̂1)q̂1 >(a� c)28b

We can solve this expression for q̂1. First, I�ll divide both sides of thisexpression by b, �

a� cb

� q̂1�q̂1 >

(a� c)28b2

and for the sake of simple algebra, let X � a�cb ,

(X � q̂1)q̂1 >X 2

8

Rearranging terms,

8(q̂1)2 � 8Xq̂1 + X 2 < 0


Preventing Entry

8(q̂1)2 � 8Xq̂1 + X 2 < 0

We have to go old school here and use the quadratic equation tosolve this for q̂1,

8X �p64X 2 � 4(8)X 24(8)

< q̂1 <8X +

p64X 2 � 4(8)X 24(8)

and we can discard the lower term to obtain,

q̂1 <2+

p2

4X =

(2+p2)(a� c)4b

=

�1+

1p2

�a� c2b

Thus, if the quantity that prevents entry isn�t too much higher thanthe monopoly (Stackelberg) quantity, the monopolist is better o¤increasing their output.


Preventing Entry

It�s also possible that q̂1 is less than the monopoly quantity, a�c2b .

In this case, just producing the monopoly level is enough to deter entryfrom a second �rm. This would not be predatory behavior at all, just anatural market process.In the environmental �eld, �rms actually lobby the government toimpose new regulations (causing the sunk cost to enter to increase) inorder to make this happen.

If q̂1 is higher than the monopoly quantity, then we have predatorybehavior from the incumbent.

The monopolist can threaten to drive the price down in the marketupon observing an entrant.This behavior is frowned upon.


Preventing Entry

In the typical entry deterrence model, the game works like this,

In the �rst stage, a potential entrant decides whether or not to enterthe market.In the second stage, upon observing entry, the incumbent decideswhether to �ght (raise their output level) or to accomodate (act as aStackelberg leader) the entrant.

Notice that the entrant gets to move �rst.


Preventing Entry

Entrant

Incumbent

EnterDo Not Enter

Fight Accomodate

(a c)2

4b

(a c)2

8b(a c)2

8b(a c)2

16b

0

Incumbent

Entrant

Ugly Number

<

F F


Preventing Entry

Entrant

Incumbent

EnterDo Not Enter

Fight Accomodate

(a c)2

4b

(a c)2

8b(a c)2

8b(a c)2

16b

0

Incumbent

Entrant

<

FUgly Number F


Preventing Entry

The incumbent can threaten to produce a higher quantity all theywant to. If the entrant gets to move �rst, it knows that theincumbent�s threat isn�t credible.

Upon observing entry, the incumbent maximizes pro�t by producingthe Stackelberg quantity, rather than q̂1.

Thus, it wouldn�t be rational to �ght entry for the incumbent in thiscase.


Capacity Commitment

How can the incumbent deter entry then?

Suppose we changed the model a little bit.

In the �rst stage, the incumbent is able to invest in capacity, i.e., theycan determine how much capital to have on hand for production.In the second stage, the entrant decides whether to enter or not.In the third stage, if the entrant enters, the �rms compete in asimultaneous (Cournot) setting.


Capacity Commitment

In the �rst stage of this new game, the monopolist chooses theircapacity level in the form of capital investment.

This is feasible because capital is �xed in the short term.They choose a capital level that allows them to produce a capacity Kat a cost of r per unit of capacity. This cost is then sunk, meaningthey pay it even if they don�t use all of their capacity.In the third stage, they then can product q1 � K , while only incurringtheir variable cost of production, w . If q1 > K , they must pay for theadditional capacity at the time of production.

Essentially, what the incumbent can do is invest early on, sinkingsome cost into capital investment that lowers their marginal cost ofproduction later on.

Sunk costs do not go into their maximization decision.


Capacity Commitment

Let�s use our standard Cournot model, where inverse demand is

p = a� b(q1 + q2)

The incumbent�s pro�t maximization problem in the third stagebecomes

maxq1

�(a� b(q1 + q2))q1 � wq1 � rK if q1 � K(a� b(q1 + q2))q1 � (w + r)q1 if q1 > K

with �rst-order condition,

∂π1∂q1

=

�a� 2bq1 � q2 � w = 0 if q1 � K

a� 2bq1 � q2 � (w + r) = 0 if q1 > K


Capacity Commitment

∂π1∂q1

=

�a� 2bq1 � q2 � w = 0 if q1 � K

a� 2bq1 � q2 � (w + r) = 0 if q1 > K

Solving these for q1 gives us our best-response function,

q1(q2) =� a�w

2b � q22 if q1 � K

a�w�r2b � q2

2 if q1 > K

Notice that if q1 < K , the intercept in the best response function ismuch higher. This corresponds to the lower marginal cost that theincumbent faces due to having pre-invested in their capacity.

As their output level exceeds their capacity, they lose that costadvantage.


Capacity Commitment

q1

q2

K q1(q2)

a w2b

a w r2b


Capacity Commitment

Whatever level of capacity the incumbent chooses to carry determineswhere the break in the best response function is.

Naturally, they lose their strategic advantage in the third stage if theyset the capacity constraint too low, so investment is typically a goodidea.


Capacity Commitment

The entrant can�t pre-commit to any capacity before the third stage,so their pro�t maximization function is

maxq2

(a� b(q1 + q2))q2 � (w + r)q2

with �rst-order condition,

∂π2∂q2

= a� bq1 � 2bq2 � (w + r) = 0

Solving this expression for �rm 2�s quantity gives us their bestresponse function,

q2(q1) =a� w � r

2b� q12


Capacity Commitment

q1

q2

q2(q1)

a w r2b


Capacity Commitment

Since the value of K can vary, it would bene�t us to look at both bestresponse functions for the incumbent at the same time.


Capacity Commitment

q1

q2

q1(q2)

a w2b

a w r2b

q2(q1)

a w r2b


Capacity Commitment

q1

q2

q1(q2)

a w2b

A

B

a w r2b C

q2(q1)

a w r2b


Capacity Commitment

Naturally, the incumbent is going to want to pick some value of Kbetween points A and B.

Picking a value for K that leads to point A induces the Cournotoutcome, where each �rm produces an output level of

a� w � r3b

Picking a value of K that leads to point C induces themonopoly/Stackelberg outcome (If K is set at that level, the bestresponse functions do cross there).Picking a value of K that exceeds point C up to point B describes theearlier setting where the incumbent threatens to overproduce.


Capacity Commitment

What ends up happening? That depends on the sunk cost to entryand how much the entrant needs to produce to break even.

Suppose the entrant�s break even quantity were above the Cournotoutput level (Point A). In this case, there is no way the entrant everenters the market, and the incumbent sets their capacity to themonopoly level (Point C )Suppose the entrant can break even at the Cournot output level (PointC ), but needs to produce more than their Stackelberg amount (PointB). In this case, again, the entrant does not enter the market, and theincumbent sets the monopoly level of capacity (Point C )

Neither of these outcomes are predatory.


Capacity Commitment

Now, suppose the entrant can break even at the Stackelberg outputlevel (Point C ).

If the entrant can break even at point B, i.e., their �xed entry cost isvery low, there�s no bene�t to the monopolist to raising their capacitylevel, as they can�t drive the entrant out of the market. Thus, itremains at the Stackelberg level (point C )If the entrant�s break even point lays between points B and C , there isroom for the monopolist to raise their quantity and drive them out ofthe market. The monopolist would be willing to set K up to

K < q̂1 =�1+

1p2

�a� w � r

2b

which would induce the entrant to not enter the market. Themonopolist then produces the monopoly quantity, not meeting their setcapacity.

If the incumbent drives the entrant out in this case, it would beconsidered predatory.


Capacity Commitment

In essence, the monopolist can invest in capacity early on, and thisserves as a signal to potential entrants.

It tells them that the incumbent has all of the tools it needs to driveprices down and make their entry into the market completelyunpro�table.

This is extremely anticompetitive, but it has happened several timesthroughout history.

Southern Bell TelephoneSafeway in Edmonton, Alberta


Summary

Sometimes, a monopolist will set their output level higher than themonopoly level if it is able to deter a potential entrant fromthreatening their market share.

This requires a credible threat in the form of capacity investment.


Next Time

Predation.

Reading: 9.3-9.5.

Midterm on Friday.


Homework 4-4

Study and work on those notecards.


econs 425 - entry deterrence - washington state university · preventing entry in the typical entry...

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