Mergers under endogenous minimum quality standard: a note

3.1 Low-quality merger: 2 and 3.

The equilibrium values are the following:

qL = 0.2533, ⅛ = 0.0483, qL = 0                    (7)

pL = 0.1076, pL = 0.0102, pL = 0                   (8)

xL = 0.5250, xL = 0.2625, xL = 0                   (9)

πf = 0.0244, ∏₂,3 = 0.00153                      (10)

θL = 0.4748, θL = 0.2125                        (11)

CS^l = 0.0433, W^l = 0.0692                    (12)

Where CS^l and W^l respectively denote consumer surplus and welfare. This
merger increases the differentiation 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 finds it profitable to eliminate the low-quality insider and the consumer
surplus does not depend on its level. Since the high-quality firm is not af-
fected by the low quality and the joint profit 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-off, in particular,
i) consumers with preferences lower than θ₂ are not covered after the merger,
ii) consumers in the range Θ^l — Θ^l after the merger receive a lower quality at a
higher price, iii) consumers in the range θɪ — θp that after the merger switch
from q₂ to q^L, 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 profit
offsets the reduction in consumer surplus. See Figure 1.

3.2 High-quality merger: 1 and 2.

The equilibrium values are:

qf = 0.25, qξ^r = 0.11198, qf = 0.09275                (13)

pH = 0.08113, pH = 0.01212, pH = 0.00502             (14)

∏_lj2 = 0.06717, πf = —0.0027                    (15)

CS ^h = 0.06256 W ^h = 0.06448                 (16)

0f = 0.5, θH = 0.36945, θH = 0.05414                (17)

θ*

³For instance, for point iii) it is straightforward to see that ʃ-£ (θ (q^) — p^^) —
Z Z      .

⅛L (θ(¾*) — P₂) = —0.03 5349

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