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

1.1 A Simple Model of Competition in Quantities 9
the same output satisfying a − 2q − (n − 1)q = c. This implies the following
output per firm as a function of n: 9
q(n) = a − c
(1.4)
n +1
with total production Q(n) =n(a − c)/(n +1), which is increasing in the
number of firms. The equilibrium price can be derived as:
p(n) = a + nc
(1.5)
n +1
which is decreasing in the number of firms and approaching the marginal cost
of production when the number of firms increases. Nevertheless, the profits
of each firm are constrained by the fixed costs of production:
π(n) =
µ 2 a − c
− F
n +1
The profits of each single firm are clearly decreasing when the number of
competitors is increasing. This suggests that in the medium and long run,
new firms will enter in the market as long as there are positive profits to
be made, and they will stop entering when the number of firmsachievesan
upper bound. This leads us to the next equilibrium concept.
1.1.3 Marshall Equilibrium
It is now extremely simple to extend the model to endogenize entry. Formally,
consider the following sequence of moves:
1) in the first stage all potential entrants simultaneously decide “in” or
“out”;
2) in the second stage all the firms that have entered choose their own
strategy q i .
In what follows we will mainly refer to F as to a technological cost of
production, but one could think of it as including other concrete fixed costs
of entry or opportunity costs of participation to the market, as the profits
that an entrepreneur can obtain in another sector. Beyond the particular
interpretation, the role in constraining entry is the same.
As we have seen, in the case of a Nash equilibrium the entry of a new
firm enhances competition leading to a reduction in the profit of each single
firm in the market. If we assume that entry takes place as long as positive
profits can be obtained, a Marshall equilibrium should be characterized by a
number of firms n satisfying a no entry condition π(n +1)< 0 and a no exit
condition π(n) ≥ 0. When the fixed cost of production is small enough, this
9 One can verify that both the cases of a monopoly and of the Cournot duopoly
are particular cases for n =1and n =2.