Chapter 11: Horizontal Mergers1 Horizontal Mergers

Chapter 11: Horizontal Mergers 1

Horizontal Mergers


Introduction

• Merger mania of 1990s disappeared after 9/11/2001

• But now appears to be returning– Oracle/PeopleSoft

– AT&T/Cingular

– Bank of America/Fleet

• Reasons for merger– cost savings

– search for synergies in operations

– more efficient pricing and/or improved service to customers


Questions• Are mergers beneficial or is there a need for regulation?

– cost reduction is potentially beneficial– but mergers can “look like” legal cartels

• and so may be detrimental• US government is particularly concerned with these

questions– Antitrust Division Merger Guidelines

• seek to balance harm to competition with avoiding unnecessary interference

• Explore these issues in next two chapters– distinguish mergers that are

• horizontal: Bank of America/Fleet• vertical: Disney/ABC• conglomerate: Gillette/Duracell; Quaker Oats/Snapple


Horizontal mergers• Merger between firms that compete in the same product

market– some bank mergers– hospitals– oil companies

• Begin with a surprising result: the merger paradox– take the standard Cournot model– merger that is not merger to monopoly is unlikely to be profitable

• unless “sufficiently many” of the firms merge• with linear demand and costs, at least 80% of the firms• but this type of merger is unlikely to be allowed


An Example Assume 3 identical firms; market demand P = 150 - Q; each firm with marginal costs of $30. The firms act as Cournot competitors. Applying the Cournot equations we know that:

each firm produces output q(3) = (150 - 30)/(3 + 1) = 30 unitsthe product price is P(3) = 150 - 3x30 = $60profit of each firm is (3) = (60 - 30)x30 = $900

Now suppose that two of these firms merge, thenthere are two independent firms so output of each changes to:

q(2) = (150 - 30)/3 = 40 units; price is P(2) = 150 - 2x40 = $70

profit of each firm is (2) = (70 - 30)x40 = $1,600

But prior to the merger the two firms had total profit of $1,800

This merger is unprofitable and should not occur


A Generalization Take a Cournot market with N identical firms.

Suppose that market demand is P = A - B.Q and that marginal costs of each firm are c.

From standard Cournot analysis we know the profit of each firm is:

Ci =

(A - c)2

B(N + 1)2

Now suppose that firms 1, 2,… M merge. This gives a market in which there are now N - M + 1 independent firms.

The ordering of the firmsdoes not matter


Generalization 2

Each non-merged firm chooses output qi to maximize profit:

i(qi, Q-i) = qi(A - B(qi + Q-i) - c)

where Q-i = is the aggregate output of the N - M firms excluding firm i plus the output of the merged firm qm

The newly merged firm chooses output qm to maximize profit:

m(qm, Q-m) = qm(A - B(qm + Q-m) - c)

where Q-m = qm+1 + qm+2 + …. + qN is the aggregate output of the N - M firms that have not merged

Comparing the profit equations then tells us:

the merged firm becomes just like any other firm in the market

all of the N - M + 1 post-merger firms are identical and so must produce the same output and make the same profits


Generalization 3 The profit of each of the merged and non-merged firms is then:

Cm = C

nm =(A - c)2

B(N - M + 2)2

The aggregate profit of the merging firms pre-merger is:

Profit of each surviving firmincreases with M

Ci =

M(A - c)2

B(N + 1)2

So for the merger to be profitable we need:

(A - c)2

B(N - M + 2)2>

M(A - c)2

B(N + 1)2this simplifies to:

(N + 1)2 > M(N - M + 2)2


The Merger Paradox Substitute M = aN to give the equation

(N + 1)2 > aN(N – aN + 2)2

Solving this for a > a(N) tells us that a merger is profitable for the merged firms if and only if:

a > a(N) = N

NN

2

4523

Typical examples of a(N) are:

N 5 10 15 20 25a(N) 80% 81.5% 83.1% 84.5% 85.5%

M 4 9 13 17 22


The Merger Paradox 2• Why is this happening?

– merged firm cannot commit to its potentially greater size• the merged firm is just like any other firm in the market• thus the merger causes the merged firm to lose market share• the merger effectively closes down part of the merged firm’s

operations– this appears somewhat unreasonable

• Can this be resolved?– need to alter the model somehow

• asymmetric costs• timing: perhaps the merged firms act like market leaders• product differentiation


Merger and Cost Synergies• Suppose that firms in the market

– may have different variable costs– incur fixed costs

• Merger might be profitable if it creates cost savings• An example

– three Cournot firms with market demand P = 150 – Q

– two firms have marginal costs of 30 and fixed costs of f

– total costs are:– C(q1) = f + 30q1; C(q2) = f + 30q2– third firms has potentially higher marginal costs– C(q3) = f + 30bq3, where b > 1


Case A: Merger Reduces Fixed Costs• Suppose that b = 1

– all firms have the same marginal costs of 30

– but the merged firms has fixed costs af with 1 < a < 2

• We know from the previous example that:– pre-merger profit of each firm are 900 – f

– post-merger • the non-merged firm has profit 1,600 - f

• the merged firm has profit 1,600 – af

• The merger is profitable for the merged firm if:– 1,600 – af > 1,800 – 2f

– which requires that a < 2 – 200/f

Merger is likely to be profitable when fixed costs are “high” and the merger gives “significant”

savings in fixed costs


Case A: 2

• Also, the non-merged firm always gains– and gains more than the merged firms

• So the merger paradox remains in one form– why merge?

– why not wait for other firms to merge?


Case B: Merger Reduces Variable Costs• Suppose that merger reduces variable costs

– assume that b > 1 and that f = 0– firms 2 and 3 merge– so production is rationalized by shutting down high-cost operations– pre-merger:

– outputs are:4

90210

4

390321

bq;

bqq CCC

– profits are:

16

90210;

16

390 2

3

2

21

bb CCC

– post-merger profits are $1,600 for both the merged and non-merged firms


Case B: 2

• Is this a profitable merger?

• For the merged firm’s profit to increase requires:

0

16

90210

16

390600,1

22

bb

• This simplifies to: 25(7 – 3b)(15b – 9)/2 > 0• first term must be positive for firm 3 to have non-negative output

pre-merger

• so the merger is profitable if the second term is positive

• which requires b > 19/15

Merger of a high-cost and low-cost firm is profitable if cost disadvantage of the high-cost

firm is “great enough”


Summary

• Mergers can be profitable if cost savings are great enough– but there is no guarantee that consumers gain

– in both our examples consumers lose from the merger

• Farrell and Shapiro (1990)– cost savings necessary to benefit consumers are much greater than

cost savings that make a merger profitable

– so should be skeptical of “cost savings” justifications of mergers

– and the paradox remains• non-merged firms benefit more from merger than merged firms


The Merger Paradox Again

• The merger paradox arises because despite merging, merged firms are symmetric with non-merged firms?

• What kind of asymmetries might arise?– merged firms become Stackelberg leaders post-merger

– By committing to merger, merged firms may induce others to merge

– Can these alterations remedy the merger paradox?


A Leadership Game• Suppose that there has been a set of two-firm

mergers– market has L leaders and F followers = N = F+L total– assume linear demand P = A – BQ– each firm has constant marginal cost of c– two-stage game:

• stage 1: each leader firm chooses its output ql independently• gives aggregate output QL

• stage 2: each follower firm chooses its output qf independently, but in response to the aggregate output of the leader firms

• gives aggregate follower output QF

• clearly, leader firms correctly anticipate QF


Leadership Game 2• Recall that

– if the inverse demand function is P = a – bQ – there are n identical Cournot firms– and all firms have marginal costs c– then each firm’s Cournot equilibrium output is:

bn

caqC

i 1

• In our example – if the leaders produce QL then inverse demand for the followers is

P = (A – BQL) – bQF – there are N - L identical Cournot follower firms– so that a = (A – BQL), b = B and n = N – L


Leadership Game 3• So the Cournot equilibrium output of each follower firm is:

111

LN

Q

LNB

cA

LNB

cBQAq LL

f

• Aggregate output of the follower firms is then:

11

LN

QLN

LNB

cALNQ L

F

• Substituting this into the market inverse demand gives the inverse demand for the leader firms:

LQ

LN

B

LN

cLNAP

11

• in this case a = (A + (N – L)c/(N – L + 1); b = B/(N – L +1) and n = L


Leadership Game 4• So the Cournot equilibrium output of each leader firm is:

1

LB

cAql

• Note that when L = 1 this is just the standard Stackelberg output for the lead firm.

• Substitute into the follower firm’s equilibrium and simplifying gives the output of each follower firm:

11*

LNLB

cAq f

• Clearly, each leader has greater output than each follower • merger to join the leader group has an advantage


Leadership Game 5• Substituting the equilibrium outputs into the inverse demand gives the

equilibrium price-cost margin and profits for each type of firm:

11

LNL

cAcP

22

2

2

2

11,;

11,

LNLB

cALN

LNLB

cALN FL

• The leaders are more profitable than the non-merged followers• Is one more merger profitable for the merging firms?• Such a merger leads to there being L + 1 leaders, F – 2 followers and

N – 1 firms in all


Leadership Game 6• So for an additional merger to be profitable for the merging firms we

need L(N – 1, L + 1) > 2F(N, L)

• This requires that (L + 1)2(N – L + 1)2 – 2(L + 2)2(N – L – 1) > 0

• Note that this does not depend on any demand parameters A, B or c

• It is possible to show that this condition is always satisfied

• No matter how many leaders and followers there are an additional two follower firms will always want to merge– this squeezes profits of the non-merged firms

– so resolves the merger paradox


Leadership Game 7• What about consumers?

• For an additional merger to benefit consumers N – 3(L + 1) > 0

• An additional merger benefits consumers only if the current group of leaders contains fewer than one-third of the total number of firms in the market.

• Admittedly this model is stylized– how to attain leadership?

– distinction between leaders and followers not necessarily sharp

• But it is suggestive of actual events and so qualitatively useful


Sequential Mergers

• It is possible to think of the merger paradox as a coordination problem. What does this mean?

• It may be the case that if enough firms complete mergers each merger will be profitable but that for small group to merge by itself is not profitable

• Consider a market with potential merger pairs:– Merger Pair 1 (Firm A and Firm B)

– Merger Pair 2 (Firm A’ and B’)

• The game may have two Nash Equilibria, one where both pairs merge and one where neither merges


Sequential Mergers 2

Merger Pair 2

Don’t Merge

Don’t Merge

Merge

Merge

($772, $772) ($1063, $752)

($752, $1063) ($1100, $1100)

This is a NashEquilibrium in

simultaneous play

This is a NashEquilibrium in

simultaneous play

($1100, $1100)

($772, $772)

Merger Pair 1

This is also a NashEquilibrium in

simultaneous play

This is also a NashEquilibrium in

simultaneous play

Ideally, the merger pairs would like to coordinate their decisions and arrive at the Both Merge equilibrium. However, with simultaneous play, it is not clear how such coordination will happen.


Sequential Mergers 3

Merger Pair 2

Don’t Merge

Don’t Merge

Merge

Merge

($772, $772) ($1063, $752)

($752, $1063) ($1100, $1100)

($1100, $1100)

Merger Pair 1

This is a NashEquilibrium in sequential play

This is a NashEquilibrium in sequential play

Sequential play with Merger Pair 1 going first solves the coordination problem. Merger Pair 2 will realize that if they merge, Merger Pair 2 will do the sameThis will make Merger Pair 1’s merger profitable


Sequential Mergers 4• The sequential merger analysis may solve the merger

paradox if the source of that paradox is a coordination problem

• The analysis has an advantage over the Stackelberg leader model because it is explicitly sequential, i.e., mergers happen in chronological sequence. In the leader model, every firm wants to become a leader simultaneously

• Cost breakthroughs or changes in transportation and trade barriers can create the setting for the sequential merger analysis

• Such events can therefore lead to merger waves


Horizontal Mergers and Product Differentiation

• Assumption thus far is that firms offer identical products• But we clearly observe considerable product

differentiation• Does this affect the profitability of merger?

– affects commitment• need not remove products post-merger

– affects the nature of competition• quantities are strategic substitutes

– passive move by merged firms met by aggressive response of non-merged firms

• prices are strategic complements– passive move by merged firms induces passive response by non-merged

firms


Merger with Price Competition• Mergers with price competition and product differentiation

are profitable• Why?

– prices are strategic complements– merged firms can strategically commit to producing a range of

products– with homogeneous products there is no such ability to commit

• unless the merged firms can somehow become market leaders


Merger with Price Competition 2• Suppose there are N firms with linear demand

• With zero marginal cost, each firm’s first order condition is

• Using symmetry we get

• If firms 1,…M merge, it will have a new first order condition:

N

1j jiiN1i pN1

pγpVp,...,pq

0pNγ

pN2γ

2γγ2pVpπ N

ij

1jjiii

i

i

1)γ(N2NNV

p0

M

mk

1k m

k

m

m

m

M

1k k

pπ

pπ

p

π


Merger with Price Competition• Because of symmetry, the prices on all the products of the

merged firms will be the same and the prices and only the nonmerged firms will bill be the same. For a not merged firm and a merged firm we have

• Using

nmm

N

ij

jj pMNMpp 1

1

p jj1

jm

N

M 1 pm N M pnm

N

pM

pm

M

mk

k m

k 1

1


Merger with Price Competition• Gives first order conditions for the nonmerged firms

• And for the merged firm

• Which gives prices

i

pnm

V 2 pnm N

Mpm M 1 pnm 0

kk1

Mpm

V 2 1 pm N

N M pnm 2Mpm

22)13(24

22

22)13(24

122

2

2

MNN

MNMNN

MNNVp

MNN

MNMNN

NNVp

nm

m


Merger with Price Competition

• The merged firm set higher prices– Since prices are strategic complements,

nonmerging firms also have higher prices• The merger is profitable for the merging firms, but

even more profitable for the nonmerging firms• The greater the number of merging firms, the

more profitable it is


A Spatial Approach

• Consider a different approach to product differentiation– spatial model of Hotelling

– products are differentiated by “location” or characteristics

– merger allows coordination of prices

– but merged firms can continue to offer the pre-merger product range

– is merger profitable?


The Spatial Model• The model is as follows

– a market called Main Circle of length L– consumers uniformly distributed over this market– supplied by firms located along the street– the firms are competitors: fixed costs F, zero marginal cost– each consumer buys exactly one unit of the good provided that its

full price is less than V– consumers incur transport costs of t per unit distance in travelling

to a firm– a consumer buys from the firm offering the lowest full price

• What prices will the firms charge?• To see what is happening consider two representative

firms


The spatial model illustrated

Firm 1 Firm 2

Assume that firm 1 setsprice p1 and firm 2 sets

price p2

Price Price

p1

p2

xm

All consumers to theleft of xm buy from

firm 1And all consumers

to the right buy fromfirm 2

What if firm 1 raisesits price?

p’1

x’m

xm moves to theleft: some consumers

switch to firm 2


The Spatial Model

• Suppose that there are five firms evenly distributed

1

2

34

5

these firms will split the market

r12

r23

r34

r45

r51

we can then calculate the Nash equilibrium prices each firm will charge

each firm will charge a price of p* = tL/5 profit of each firm is then tL2/25 - F


Merger of Differentiated Products

1 2 3 4 5

Price

Main Circle (flattened)

r51 r12 r23 r34 r45 r51

now consider a merger between some of these firms

a merger of non-neighboring firms has no effect

A merger of firms2 and 4 does

nothing

but a merger of neighboring firms changes the equilibrium

A merger of firms2 and 3 doessomething


Merger of Differentiated Products

1 2 3 4 5

Price

Main Circle (flattened)

r51 r12 r23 r34 r45 r51

merger of 2 and 3 induces them to raise their prices

so the other firms also increase their prices

the merged firms lose some market share what happens to profits?


Spatial Merger (cont.)

The impact of the merger on prices and profits is as follows

Pre-Merger Post-Merger

Price Profit Price Profit

1

2

3

4

5

tL/5 tL2/25

tL/5 tL2/25

tL/5 tL2/25

tL/5 tL2/25

tL/5 tL2/25

1

2

3

4

5

14tL/60 49tL2/900

19tL/60 361tL2/7200

19tL/60 361tL2/7200

14tL/60 49tL2/900

13tL/60 169tL2/3600


Spatial Merger (cont.)• This merger is profitable for the merged firms• And it is not the best that they can do

– change the locations of the merged firms• expect them to move “outwards”, retaining captive consumers

– perhaps change the number of firms: or products on offer• expect some increase in variety

• But consumers lose out from this type of merger– all prices have increased

• For consumers to derive any benefits either– increased product variety so that consumers are “closer”– there are cost synergies not available to the non-merged firms

• e.g. if there are economies of scope• Profitability comes from credible commitment


Price Discrimination What happens if the firms can price discriminate? This leads to a dramatic change in the price equilibrium

t ti i+1

take two neighboring firms

s

consider a consumer located at s

Pricep1

i

suppose firm i sets price p1i

i+1 can undercut with price p1i+1

p1i+1

i can undercut with price p2i

p2i

and so oni wins this competition by “just” undercutting i+1’s cost of supplying s

p*i(s)

the same thing happens at every consumer locationequilibrium prices are illustrated by the bold lines

Firm i suppliesthese consumers

and firm i+1these consumers


Merger with price discrimination Start with a no-merger equilibrium

1 2 3 4

Price equilibriumpre-merger is given

by the bold lines

Profit for each firmis given by theshaded areas

This is much betterfor consumers than no price discrimination


Merger with price discrimination Now suppose that firms 2 and 3 merge

1 2 3 4

They no longer compete in prices so the price equilibrium changes Prices to the captiveconsumers between

2 and 3 increaseProfits to themerged firms

increase

This is beneficial for the merged firms but harms

consumers


Public Policy and Horizontal Mergers• Antitrust authorities consider the unilateral effects

discussed above and coordinate effects– A merger may make collusion easier

• Consider– Number of firms– Cost structures across firms– Entry barriers


Public Policy and Surplus• Focus is generally on Consumer surplus

– Ignores profits to merging firms– And to their competitors

• Most economic theory favors a measure of total surplus, but..– Distributional concerns favor consumer surplus– Firms may exaggerate cost savings, and consumers are not

represented at proceedings• Also, firms may have a choice among mergers

– Having a criteria of consumer surplus will push them towards ones with higher total surplus since they favor ones with higher producer surplus


Empirical Application: Merger Simulation• Antitrust evaluation of a proposed merger requires some

prediction of prices and outputs in the post-merger market• One way to make such a prediction is to build a

mathematical model of the post-merger market and to simulate its workings on a computer

• Merger simulation is a combination of economic modeling and econometric estimation– Economic modeling reflects standard maximizing behavior in the

context of strategic interaction to characterize the post-merger equilibrium

– Econometric estimation is required to obtain realistic values for the key parameters of the economic model


Merger Simulation 2• Consider a product-differentiated market before any• First-order condition for each firm i is:

01

iii

ii

p

cp

0 iiiii ss • Note: Market share and price are observable and relatively easy to measure. Cost is difficult to know. But if we have an estimate of the elasticity, then cost can be inferred from the above relationship.

• Here ii the (negative of the) elasticity of the firm’s demand with respect to its own price.

• Defining the price-cost margin as ii and the firm’s market share as sii this may be rewritten as


Merger Simulation 3• If two firms, say firms 1 and 2, merge and if they continue to

market both products, they will now coordinate the pricing of each good to maximize the combined profits

• The two first order conditions now are:

0212211111 sss

0121122222 sss• Assuming market shares do not change “too much”, it is easy to see how the knowledge of the relevant own- and cross-price elasticities, along with the estimates of marginal cost from the pre-merger data can be used to work out the price-cost margins and therefore the prices in the post-merger world• What is key is getting estimates of all the relevant elasticities


Merger Simulation 4• Estimating all the relevant elasticities though is a tall order

– Need to specify a demand system– Need to link demand parameters to elasticities

• Usual to specify an almost ideal demand system (AIDS). If there are four pre-merger firms this system is:

44434324214144

43433323213133

42432322212122

41431321211111

lnlnlnln

lnlnlnln

lnlnlnln

lnlnlnln

pbpbpbpbas

pbpbpbpbas

pbpbpbpbas

pbpbpbpbas

• It is easy to show how the bij coefficients may be translated into

corresponding ij elasticities. Still it is clear that even ignoring the aij intercept term, estimating the relevant elasticities for an n firm market requires obtaining estimates for n2 parameters.


Merger Simulation 4• Estimating n2 parameters with precision is difficult• So, the typical estimation procedure usually imposes

additional structure on the market model. • For example, Proportionally Calibrated AIDS assumes that

the sales loss by a firm when it raises its price is translated to rivals in proportion to their market shares.

• This removes the need to estimate the cross-elasticities• However, such structural restrictions are not without

consequences. • Depending on the precise demand specification and cross-

elasticity restrictions, Slade (2008) find differences in post-merger predictions as high as 40 percent

• MORAL: Merger simulation is as much art as science and requires great care in implementation & interpretation


Merger Simulation 5• Even if agreement can be reached on simulation technique,

different techniques are available for estimating the needed elasticities and these two can lead to great variation in post-merger outcomes

• Staples-Office Depot Merger is a good example– Are the relevant competitors to a retail office supply store all

the other suppliers in a standard metropolitan area, or;

– Does the strength of competition decline as the rival firm is located farther from the store under consideration?

• Producing clear, statistical evidence that non-economists and the courts can easily assess is very difficult

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Chapter 11: Horizontal Mergers1 Horizontal Mergers