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

1.1 A Simple Model of Competition in Quantities 7
strategy before the rival, it can use this power to increase profits excluding
entry. 7 Moreover, if this firm remains alone in the market, it could be able
to restore the monopolistic price in the future. When this is the case, the
exclusionary strategy ends up increasing the final price, therefore antitrust
authorities should punish it as a predatory strategy.
Collusion. A third way to increase profits requires collusion. To see how
it works in our simple setup, let us go back to the symmetric duopoly. The
reduction in total profits associated with Cournot competition (compared
to the monopolistic outcome) was due to the fact that each firm did not
take into consideration the impact of its own production on the profits of
the other firm, and hence tended to produce too much from the point of
view of joint profit maximization. This externality leads to a price reduction
and to a decline in total profits. For this reason the two firms may try to
collude and agree on limiting their production at a lower level, possibly at
the monopolistic level. Under perfect collusion, each one of the two firms
produces half of the monopolistic output, ˜q =(a − c)/4, andobtainsprofits
˜π =(a − c) 2 /8 − F .
However, only a strong and reciprocal commitment could guarantee that
such a collusive behavior is sustainable, because in the absence of a commitment
each firm would have incentives to deviate and produce more than
that. For instance, if a firm is sure that the other one produces at the collusive
level, this firm can deviate from the collusive strategy and choose an
output q D that maximizes π =(a − q D − ˜q)q D − cq D − F .Theoptimaldeviation
is exactly q D =3(a − c)/8. After deviating from the collusive strategy,
this firm increases its profits to π D =9(a − c) 2 /64 − F , which is above the
collusive profits, while the profits of the other firm are reduced below them.
This profitable deviation should not surprise, because there must be always
aprofitable deviation for each firm when we are not in the Cournot equilibrium.
Not by chance, we can also provide an alternative definition of the
Cournot equilibrium as one in which there are not profitable deviations for
any firm.
It is important to notice that collusive outcomes can be reached more
easily when interactions are repeated over time, because deviations can be
punished in the future, and the threat of punishments can reduce the incentives
to deviate. The theory of collusion has studied the conditions under
which monopolistic profits can be sustained in dynamic games. For instance,
if the same competition is repeated infinite times, each firm discounts the
future, and each deviation is punished with reversion to the Cournot equilibrium
forever, collusion is sustainable if and only if firms are patient enough.
7 Notice, however, that the exclusionary strategy does not necessarily increase the
price and, even if it increases the price, it does not necessarily reduce welfare
(measured as consumer surplus plus profits). If the fixed cost of production is
high enough, entry deterrence may require a higher price but it may be more
efficient from a welfare point of view.