Mergers under endogenous minimum quality standard: a note

Utility of consuming product i is U = θq_i — p_i.

We add two initial stages to the timing in Scarpa (1998): in the first, the
regulator chooses wether to apply a MQS, in the second firms decide i) whether
to merge and the firm to merge with, or ii) exit the market (if the expected
profit is negative), they compete in quality and price respectively in the third
and the fourth stage.

Merging strategy entailing that: i) firms merge when the profit of the new
merged entity (insiders’ joint profits) is higher than the sum of the profits gained
by each insider without the merger, ii) each firm chooses the insider that allows
the highest profit for the merged entity.¹ We call insider each merging firm
and outsider the not merging one. As in Motta (1993) each merged entity sets
qualities and prices to maximize the insiders’ joint profits. The equilibrium is
subgame perfect.

3 The equilibrium of the model

We only focus on mergers between firm 1 and 2, called high-quality merger, and
between firm 2 and 3, low-quality merger. The reason for this choice is that in
reality mergers among firms 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 firms’ 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 ∏ij, with i = j,
be the merged entity’s profit. We report the equilibrium in Scarpa (1998):

CS* = 0.0443, W * = 0.0691                      (6)

¹We do not explicitly introduce the analysis of an efficient splitting profit mechanism
among insiders, however when the merged entity’s profit is higher than the sum of the profit
each insider gains without the merger, then it is always possible a splitting profit mechanism
making each merger profitable.

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.

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