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

1.1 A Simple Model of Competition in Quantities 13
less than the above cut-off the number of entrants will be determined by a
free entry condition. In this last case, ignoring the integer constraint on the
number of firms, 12 we can approximate the number of firmsasarealnumber
that satisfies π(q L ,n)=0. This implies:
n = a − c − q L
√
F
(1.12)
When this is the endogenous number of firms, each one of the followers is
producing:
µ
q q L , a − c − q
L
√ = √ F
F
which is independent from the strategy of the leader. Hence, the higher the
production of the leader, the lower the number of entrants, while the production
of each one of them will be the same. This would imply a constant level
of total production Q = q L +(n − 1)q(q L ,n)=a − c − √ F , and a constant
price p = a − Q = c + √ F , which would be equivalent to the equilibrium
price emerging under Marshall competition.
After having derived the behavior of the followers, it is now time to move
to the first stage and examine the behavior of the leader. First of all, let us
remind ourselves that entry takes place only for a production level which is
not too high. If this is the case, the profits of the leader must be:
π L = pq L − cq L − F = q L
√
F − F if qL