We introduce merging strategies and endogenous MQS, borrowed from Ecchia and Lambertini (1997), in Scarpa (1998). MQS induces the low-quality firm to exit the market and leads to a monopoly arising from the bilateral merger of the high-quality firmsMergers, Minimum quality standard, Quality differentiation.

Berardino Cesi

English

Research Papers in Economics

     
 
 
  
  
Volume 30, Issue 4 
  
Mergers under endogenous minimum quality standard: a note 
  
 
 
Berardino Cesi  
University of Bristol 
Abstract 
We introduce merging strategies and endogenous MQS, borrowed from Ecchia and Lambertini (1997), in Scarpa 
(1998). MQS induces the low-quality firm to exit the market and leads to a monopoly arising from the bilateral merger 
of the high-quality firms
I would like to thank Alberto Iozzi, Sara Biancini, Dimitri Paolini and the anonymous referee for their helpful comments. 
Citation: Berardino Cesi, (2010) ''Mergers under endogenous minimum quality standard: a note'', Economics Bulletin, Vol. 30 no.4 pp. 
3260-3266. 
Submitted: Sep 23 2010.   Published: December 05, 2010. 
 
     1 Introduction
The literature on minimum quality standard (MQS) has not considered the
possibility that ￿rms merge. We extend the Bertrand triopoly model of Scarpa
(1998), by allowing mergers and an MQS as in Ecchia and Lambertini (1997).
Ecchia and Lambertini (1997) show that an MQS is welfare increasing, because
it makes price collusion more di¢ cult. We show, instead, that when endogenous
horizontal mergers are allowed, an MQS becomes a welfare reducing device. This
is because the two highest quality ￿rms merge and become a monopoly, with
the lowest quality ￿rm exiting.
We add two initial stages to the timing in Scarpa (1998). In the ￿rst stage
the regulator chooses wether to introduce an MQS; in the second stage, ￿rms
decide whether to merger; in the third and fourth stage, ￿rms compete in quality
and price, respectively.
We ￿rst show that a merger between the lower quality ￿rms, although reg-
ulated by an MQS, reduces both consumer surplus and welfare. This merger
shuts down the lowest quality ￿rm and increases di⁄erentiation between the two
remaining qualities. All consumers are worse-o⁄ with the increase in aggregate
pro￿t being larger than the reduction in consumer surplus. Then we show that
such a merger never occurs in equilibrium, because a merger between the two
higher quality ￿rms is the most pro￿table. The two highest quality ￿rms pre-
fer merging under an MQS because the regulated quality will be su¢ ciently
high to induce the lowest quality ￿rm to exit the market. When an MQS is
introduced, the merger between the two highest quality ￿rms would increases
both consumer surplus and welfare then it would be preferred by the regulator,
thought the lowest quality ￿rm would gain a negative pro￿t. However, it never
occurs in equilibrium because the low-quality ￿rm exits after the announce of
an MQS. Since no bilateral merger involving the low-quality ￿rm occurs, an
MQS induces the two high-quality ￿rms to monopolize the market. On the
other hand, absent regulation a monopoly-merger among the three ￿rms arises
and induces the same welfare and consumer surplus than the equilibrium under
an MQS. Our result is in line with Ecchia and Lambertini (1997). Both papers
study the e⁄ect of an MQS on an element, collusion in their case and horizontal
relations in ours, that is usually considered by the antitrust authorities compe-
tition reducing. Endogenizing the merging strategy allows us to show that an
MQS may reduce competition becomes a welfare reducing instrument.
2 The model
Scarpa (1998) considers a two-stage triopoly with vertically di⁄erentiated qual-
ities (qi; with i = 1;2;3 and q3 < q2 < q1). Each ￿rm supplies one quality and
each consumer consumes one product. Each ￿rm i produces xi. The costs are
ci =
(qi)
2
2 with pro￿t ￿i = pixi ￿ ci. Consumers are di⁄erentiated according
to their quality preference ￿ that is uniformly distributed over [0;1], with e ￿i be
the marginal consumer; that is, the lowest consumer type that buys quality i.
1Utility of consuming product i is U = ￿qi ￿ pi.
We add two initial stages to the timing in Scarpa (1998): in the ￿rst, the
regulator chooses wether to apply a MQS, in the second ￿rms decide i) whether
to merge and the ￿rm to merge with, or ii) exit the market (if the expected
pro￿t is negative), they compete in quality and price respectively in the third
and the fourth stage.
Merging strategy entailing that: i) ￿rms merge when the pro￿t of the new
merged entity (insiders￿joint pro￿ts) is higher than the sum of the pro￿ts gained
by each insider without the merger, ii) each ￿rm chooses the insider that allows
the highest pro￿t for the merged entity.1 We call insider each merging ￿rm
and outsider the not merging one. As in Motta (1993) each merged entity sets
qualities and prices to maximize the insiders￿joint pro￿ts. The equilibrium is
subgame perfect.
3 The equilibrium of the model
We only focus on mergers between ￿rm 1 and 2, called high-quality merger, and
between ￿rm 2 and 3, low-quality merger. The reason for this choice is that in
reality mergers among ￿rms whose qualities are close are more likely to occur.2
Such a merging behavior could be usually referred in reality to as a "merger
of equals". Both ￿rms￿single brands are surrendered and a new company (the
new merged entity) is issued in their place. Since mergers are endogenous we
cannot ex ante exclude a monopoly merger in equilibrium. Let ￿i;j, with i 6= j,
be the merged entity￿ s pro￿t. We report the equilibrium in Scarpa (1998):
q￿
1 = 0:2526;q￿
2 = 0:0497;q￿
3 = 0:0095 (1)
p￿
1 = 0:1060; p￿
2 = 0:0091; p￿
3 = 0:0009 (2)
x￿
1 = 0:5225; x￿
2 = 0:2721; x￿
3 = 0:1136 (3)
￿￿
1 = 0:0235; ￿￿
2 = 0:0012;￿￿
3 = 0:00005 (4)
e ￿￿
1 = 0:477; e ￿￿
2 = 0:204; e ￿￿
3 = 0:094 (5)
CS￿ = 0:0443; W￿ = 0:0691 (6)
1We do not explicitly introduce the analysis of an e¢ cient splitting pro￿t mechanism
among insiders, however when the merged entity￿ s pro￿t is higher than the sum of the pro￿t
each insider gains without the merger, then it is always possible a splitting pro￿t mechanism
making each merger pro￿table.
2EasyJet-Go Fly and Ryanair-Buzz are examples of low-quality mergers, while Delta-
Northwestt, Alitalia-Airone and Lufhtyansa-Brusselles Airlines are example of high-quality
mergers.
23.1 Low-quality merger: 2 and 3.
The equilibrium values are the following:
qL
1 = 0:2533;qL
2 = 0:0483;qL
3 = 0 (7)
pL
1 = 0:1076; pL
2 = 0:0102; pL
3 = 0 (8)
xL
1 = 0:5250; xL
2 = 0:2625; xL
3 = 0 (9)
￿L
1 = 0:0244; ￿2;3 = 0:00153 (10)
e ￿L
1 = 0:4748; e ￿L
2 = 0:2125 (11)
CSL = 0:0433; WL = 0:0692 (12)
Where CSL and WL respectively denote consumer surplus and welfare. This
merger increases the di⁄erentiation between high-quality products and is prof-
itable for the insiders and the outsider. This scenario replicates the same results
without regulation in Motta (1993) and Barbot (2007) because the new merged
entity ￿nds it pro￿table to eliminate the low-quality insider and the consumer
surplus does not depend on its level. Since the high-quality ￿rm is not af-
fected by the low quality and the joint pro￿t of 2 and 3 is maximized when
the lowest quality is zero, then a regulator that maximizes welfare optimally
chooses to eliminate the low quality. All consumers are worse-o⁄, in particular,
i) consumers with preferences lower than e ￿2 are not covered after the merger,
ii) consumers in the range e ￿L
1 ￿ e ￿L
2 after the merger receive a lower quality at a
higher price, iii) consumers in the range ￿￿
1 ￿ e ￿L
1 , that after the merger switch
from q￿
2 to qL
1 , receive a higher quality but at a higher price, and iv) consumers
of the highest quality, with and without the merger, receive a higher quality at
a higher price.3 In such a regulated merger the increase in the aggregate pro￿t
o⁄sets the reduction in consumer surplus. See Figure 1.
3.2 High-quality merger: 1 and 2.
The equilibrium values are:
qH
1 = 0:25;qH
2 = 0:11198;qH
3 = 0:09275 (13)
pH
1 = 0:08113; pH
2 = 0:01212; pH
3 = 0:00502 (14)
￿1;2 = 0:06717; ￿H
3 = ￿0:0027 (15)
CSH = 0:06256 WH = 0:06448 (16)
e ￿H
1 = 0:5; e ￿H
2 = 0:36945; e ￿H
3 = 0:05414 (17)
3For instance, for point iii) it is straightforward to see that
R ￿￿
1
e ￿L
1
￿
￿
￿
qL
1
￿
￿ pL
1
￿
￿
R ￿￿
1
e ￿L
1
￿
￿
￿
q￿
2
￿
￿ p￿
2
￿
= ￿0:035349
3This merger is pro￿table, however MQS induces a low quality higher than the
unregulated one by leading to a strong reduction in the di⁄erentiation between
the high qualities and a slight increase in the di⁄erentiation between the low
qualities. Although such a merger increases the market coverage the regulated
quality is so high that the low-quality ￿rm obtains a negative pro￿t therefore it
would leave the market.
3.3 Monopoly mergers
When ￿rm 3 exists the market the high-quality merger leads to a monopoly in
which the MQS is applied to ￿rm 2. The merger between 1 and 2 leads to:
pM
1 =
1
2
q1 pM
2 =
1
2
q2 (18)
qM
1 = 0:25; qM
2 = 0 (19)
￿M
1;2 = 0:03125 (20)
CSM = 0:03125; WM = 0:0625 (21)
This merger is clearly pro￿table and all consumers are worse-o⁄: i) half
consumers are now out of the market, ii) consumers that consume the highest
quality even after the merger pay more for a lower quality. However, if the reg-
ulator did not announce the MQS, then ￿rms would always choose a monopoly
merger. Since the consumers surplus is only a⁄ected by the high quality, then
any monopoly (arisen from a three-￿rm or a bilateral merger) induces the same
4quality. Thus the results with and without regulator are the same of (19) and
(21).4
Proposition 1 In equilibrium only monopoly mergers occur with and without
MQS.
A merger involving the low-quality ￿rm never occurs because ￿rm 2￿ s strat-
egy of merging with the high-quality ￿rm is strictly dominant. For the high-
quality ￿rms (1 and 2) a bilateral merger under an MQS is more pro￿table than
a bilateral merger without regulation. Moreover, without regulation they prefer
a monopoly merger to a bilateral merger. Since no bilateral merger with ￿rm 3
occurs, an MQS induces the low-quality ￿rm to exit the market and leads to a
monopoly. Thus in equilibrium the monopolization of the market occurs with
or without a MQS.
4 Conclusions
When endogenous mergers are allowed, if a welfare maximization regulator
chooses an MQS as in Ecchia and Lambertini (1997) in Scarpa￿ s (1998) model,
then the market ends up being monopolized and the lowest quality ￿rm exits.
4Our results con￿rm Scarpa (1998) in the matter of the relation between the e¢ cient
number of ￿rms and the lowest quality.
5References
[1] Barbot, C. (2007) "Horizontal Mergers and Vertical Di⁄erentiation" Icfai
Journal of Mergers & Acquisitions 4, 29-40.
[2] Ecchia, G and L. Lambertini (1997) "Minimum Quality Standards and Col-
lusion" The Journal of Industrial Economics 45, 101-113.
[3] Motta, M and J.F. Thisse (1993) "Minimum Quality Standards as an Envi-
ronmental Policy: Domestic and International E⁄ects" Nota di lavoro 20.93,
Fondazione Eni Enrico Mattei, Milan.
[4] Motta, M. (1993) "Endogenous Quality Choice: Price Vs. Quantity Compe-
tition" The Journal of Industrial Economics 41, 113-131.
[5] Scarpa, C. (1998) "Minimum Quality Standards with More Than Two
Firms" International Journal of Industrial Organization 16, 665-676.
6

Mergers under endogenous minimum quality standard: a note

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