Competition, Innovation, and Antitrust. A Theory of Market ... - Intertic

1.4 A Simple Model of Competition for the Market 29
of product market competition has a negative impact on the current profits
K, while it has no impact on the value of the innovation (since this is drastic
and the innovator will not be constrained by product market competitors), it
clearly follows that an increase in the intensity of competition reduces K and
increases the investment of the monopolist and the probability of innovation
z M .AghionandGriffith (2005) put a lot of emphasis on this effect, which
they label escape competition effect:
“competition reduces pre-innovation rents...but not their post innovation
rents since by innovating these firms have escaped the fringe.
This,inturninducesthosefirms to innovate in order to escape competition
with the fringe.” 28
Now, consider a Nash equilibrium with a general number of firms. If the
incumbent does not invest, the equilibrium is the same of the symmetric
model, but the expected profit of the monopolist π M (z M ) must be:
√ √
2F (1 − 2F )K
π M (0) = K +
V
which is increasing in K (decreasing in the intensity of competition) and
decreasing in the value of the innovation V (since this increases the incentives
of other firms to innovate and replace the monopolist).
If the monopolist is investing, however, the first order conditions for the
monopolist and for the other firms in Nash equilibrium would be:
z =(1− z) n−2 (1 − z M )V ,
z M =(1− z) n−1 V − (1 − z) n−1 K
which always imply a lower investment of the monopolist because of the
Arrow effect. For instance, with two firms we have:
z M =
(1 − V )(V − K)
1 − V (V − K)
z =
(1 − V )(V − K)+K
1 − V (V − K)
(1.44)
It is interesting to verify what is the impact of an increase in the intensity of
product market competition, which lowers current profits K without affecting
the value of the drastic innovation V : this increases the investment of the
incumbent according to the escape competition effect, but it decreases the
investment of the outsider. 29
28 See Aghion and Griffith (2005, pp. 55-56). An increase of the intensity of competition
is associated with a lower price of the competitive fringe or with a higher
probability of entry of equally efficient firms.
29 Of course, the Arrow effect could be counterbalanced if we introduced a technological
advantage for the incumbent (Barro and Sala-i-Martin, 1995) or absorptive
capacity of the incumbent (Wiethaus, 2006,a,b), that is the ability to
imitate the innovation of an outsider.