Review of Industrial Organization 16: 89–95, 2000.
© 2000 Kluwer Academic Publishers. Printed in the Netherlands.
The Dominant Firm Model Revisited
Department of Economics, Brooklyn College Brooklyn, NY 11210-2889, U.S.A.
Abstract. This paper extends the standard Forchheimer dominant ﬁrm model by making more
explicit shifts in the fringe supply when the market price set the dominant ﬁrm deviate from its
limit price. It demonstrated how, when a dominant ﬁrm engages in short-run proﬁt maximization, the
market price it sets in the long run will equal its limit price and that, in certain situations, increased
production cost for fringe lead to an increase in the number of fringe ﬁrms in the long run.
During the 1960s and 1970s, there was a standard presentation of the dominant
ﬁrm model. As stated by Shepherd (1997, p. 206), it assumed that “there existed
fringe ﬁrms, each one of them being tiny and all of them collectively adding up to a
minor share of the market. Their collective supply curve is subtracted horizontally
from the market demand, to give the dominant ﬁrm’s own demand curve”.
Beginning in the 1980s, this model fell into disfavor for a variety of reasons.
First, some authors presume that if the dominant ﬁrm is the low-cost producer it
will become a monopolist by bankcrupting all of the fringe ﬁrms. For example,
Clarkson and Miller (1982, p. 193) contend that the dominant ﬁrm would accede
to allowing fringe ﬁrms to survive only to avoid anti-trust legislation but end their
discussion: “Note that if there are great differences between high-cost ﬁrms and
low-cost ﬁrms, the high cost ﬁrm will not recover full costs and will gradually be
eliminated from the industry”.
The suggestion that a low-cost producer will always ﬁnd it most proﬁtable
to eliminate its competitors is consistent with Jean Tirole’s presentation of the
Bertrand Paradox (1988, pp. 210–212). As Clarkson and Miller, Tirole posits two
ﬁrms who will equally divide the market if they charge the same price. However,
suppose that Firm 1 has constant marginal cost equal to c
, which is less than the
constant marginal cost of Firm 2 equal to c
. Tirole notes that if the Firm 1 was a
monopolist, proﬁts are maximized when (p − c
)[D(p)] is maximized, where p =
price set, and D(p) is market demand. Let p
equal the maximizing price.
Tirole then looks at two cases: If (I) p
and (II) p
Case I is straightforward. Firm 1 sets market price at p
which drives Firm 2 out
of business. Case II is a bit more complex. If Firm 1 sets p
it will not maximize
I would like to acknowledge the helpful suggestions made by Igmar Nyman and two anonymous