1
ON THE NATURE AND SIGNIFICANCE OF COLLUSIVE PRICE LEADERSHIP
by
Leo SLEUWAEGEN
(INCAP- K.U.
Leuven)·
/
ABSTRACT
With the
help of
a simple analytical model we are able to
analyze and to further clarify the conditions for collusive
price
leadership
as
they were originally
devised by Jesse
Markham. Within the confines of this model we show how collusion
increases
price
cost margins,
but
at
the same
time
decreases concentration in the industry.
INdustry
and
Louvain.
I
Crombrugghe,
which
have
Company
am
Analysis
grateful
and
two
to
Raymond
anonymous
considerably
arguments in·this paper.
Program,
improved
De
Bondt,
referees
the
University
for
Denis
of
de
suggestions
exposition
of
the
2
On the nature and si
1.
ificance of collusive
rice leadershi
Introduction
The price leadership model has recently regained a renewal
of
interest
among
industrial
economists.
Research
centers
around the basic problem of who will adopt the positions of
leaders and followers
cartel
of
price
in the industry, and to what extent a
leaders
will
be
stable
(see,
e.g.
(1978), Boyer and Moreaux (1982),
d'Aspremont et al.
Donsimoni
and
McLeod
Also
plications
of
the model
(Geroski
not
(1984)).
and Jacquemin
always
produce
are
the
( 1984)).
However,
unequivocal
(1983),
the /dynamical
subject
of
intense
these
results.
Ono
im-
debate
studies did
Much
of
the
controversy about some of the results seems to depend on the
particular
assumptions
within the industry.
focusing
on
made
about
the
behaviour
of
firms
-
In this connection the ongoing debates
collusive
price
leadership
sometimes
overlook
some of the basic conditions characterizing the emergence of
this
type
of
market
arrangement,
as
they
were
originally
exposit
some
arguments which
devised by Jesse Markham (1951).
The
aim
of
this
paper
is
to
illustrate the importance of Markham's original conditions.
We consider this analysis necessary,
because the importance
of these conditions seems not to have been fully appreciated
3
in subsequent research,
responding
(1952),
In
to
as revealed by some of the comments
Markham's
original
article
(e.g.
Oxtenfeldt
Lanzilotti (1957)).
section
2 of the paper we show the effect of enforcing
collusion among the leading firms in the industry on the degree of monopoly power in the industry. The relationship implies a combined effect of two different concentration measures,
the concentration ratio
dominant
show
firms)
that
the
and the
( Ck,
k being the number of
Hirschman-Herfindahl
explicit
distinction
(H)
between
index.
these
We
two
different concentration measures is not trivial, but becomes
i~dustries
crucially important for highly concentrated
few
large
firms
dominate
the
industry.
In
section
where
we
3
analyze how concentration may create incentives to collude.
However,
no
concentration ,as a structural quantity measure,
exogenous
show
how
determinant
of
concentration
is
oligopolistic conduct within
performance.
endogenously
the
industry.
In
section
determined
By
4
is
we
by
numerically
solving the model we then illustrate how strict enforcing of
co 11 us ion
entail
among
higher
industry.
the
members
profits
with
of
the
lower
dominant
carte 1
concentration
in
wi 11
the
4
In the new view on the relationship between market structure
and
oligopolistic conduct
performance
role.
However,
of conduct,
plays
a predominant
in spite of the recognition of the importance
very few studies
motivations of the firms
exception
to
have analyzed the behavioural
within the industry.
and
early
this
observation
who
asserted
that
oligopolists
consequently,
will
prefer
the
are
A well known
is Stigler
profit
(1964)
maximizers
collusive solution
and,
above
all
others. However, because of the tendency of individual firms
to
'chisel',
i.e.
to
engage
in
secret
price
cutting
in
order to increase individual market shares and profits,
the
actual
the
outcome - 1n
the
collusive
equilibrium.
enforcing
the
joint
considered to be an
market
In
may
Stigler's
profit
be
different
view
maximizing
information
the
problem
solution
(detection)
from
is
problem.
of
thus
Based
upon this view, John Cubbin (1982) related the set of stable
industry price-cost margins to the degree of imperfection of
collusion,
measured
in
terms
of
reaction
probabilities
or
retaliation lags reflecting information defects.
Although the model has more relevance for product-differentiated industries,
to
it is interesting to apply Cubbin's model
the collusive price-leadership model.
Particularly,
this
approach enables us to illustrate the importance of the five
conditions for the occurence of this type of oligopoly , as
they where originally devised by Jesse Markham.
Apparently,
5
because of
some
of
the lack of analytical
the
conditions
seemed
tools,
not
the importance of
to
have
been
fully
appreciated by those who commented upon their relevance.
To
show this,
largest
the
the
=
F(p)
q.
industry,
group can
represents
=
the
G(p)
as
=E
by q
and
the global demand function
the supply function
qo
quantities
[p/G(p)] [dG(p)/dp]
Denoting quantity
The demand function
then be written
define
there are n firms and that the k
industry.
and qc
competitive fringe.
Next
that
dominate
price by p,
to
assume
=
of the
facing the dominant
q -
qc
=
F ( p)
[dF(p)/dp] [p/F(p)]
-
G ( p) .
=
and
as respectively the absolute value of
elasticity of industry demand and the elasticity of supply
of the
co~petitive
fringe.
Under these conditions it follows that the elasticity of demand for
the k
largest
(dominant)
firms
equals
(see Saving
(1970)):
=
~D
l
(~
+ (1- Ck)E)
(l)
Ck
In line with Cubbin's analysis,
ding firms
lowerl.ng
their
expect
that
react
by
(leading
believe that
price
with
a
firm's)
they can increase their profits by
(increasing
certain
retaliatory
we now assume that all lea-
quantity
probability
price
price-cost
the
a
others
reductions.
margin
will
sold),
The
equal
will
and
not
resulting
a
weighted
6
combination of the (noncooperative) Cournot and perfect collusive outcome with a as the weight factor:
=
Ai
l
[a+
(l -
= i:,
i
a)soi]
... ,k
(2)
~D
= qi/qo,
where SDi
firm i's share of the quantity sold by
the dominant group
Result (2) can also be obtained from a conjectural variation
model (see Clark and Davies (1982)). Without discussing these different approaches here,
lays in
its role
~s
the essence of a in the model
characterising the degree of
(apparent
or implicit) collusion in the industry.
Since the n-k remaining firms of the competitive fringe act
as price-takers their corresponding Lerner index necessarily
or Ai
equals zero,
=
0;
i
=k + 1'
... '
n.
By weighting the
Lerner index for the k dominant firms and the n-k remaining
firms
with
their
respective
market
shares
we
obtain
the
following measure of monopoly power for the industry:
n
A =
i
where
Hk
~
=
SiA i
~
+
( 3)
+
k
=
~
i
the)
= aCk 2
l
=1
Si2
the truncated (leading firm component of
Hirschman-Herfindahl index.
one assumes competitive
If (as Hause
fringe firms to be very
n
(1977) did)
small,
Hk
7
approximately equals
:'1
=
H
~
i
Below
Herfindahl index.
=l
s12
the ordinary
we shall
discuss
Hirschmanthis
in
more
detail.
It
can
easily be
seen
Saving's
collusive
(1977).
Encaoua
from
relation
holds,
result
collusive equilibrium,
which amounts
of the two extreme solutions.
relation
reduces
(3)
respect
to
squared,
find
1
Hause
non-collusive
to a weighted average
Moreover,
to
the
for Ck
basic
approaching
(no
which
discussion
the
concentration measures,
we
0
competitive
oligopoly model (see Cubbin (1983)).
fringe)
With
=
a
(1980)
Jacquemin's
and
with
=
holds. With 0 < a < 1, we have a partially
(Cournot) result
one,
and
with a
that
(3)
/
of
the
H (approximating Hk for k<n)
two
or Ck-
is more appropriate to explain price-cost margins,
that
specification,
relation
provides
(3)
involving
weighted
a
a
more
flexible
combination
of
both
measures, with a the empirically estimable weight.
Distinguishing
the
roles
measures is not trifling,
literature,
but
of
the
separate
concentration
as is sometimes suggested in the
becomes
crucially
important
industry performance for these industries where
firms
hold
illustrated
ratio.
a
in
large
share
Figure
1
of
for
the
the
market.
four-firm
to
assess
the leading
The
point
is
concentration
8
FIGURE 1
THE HORN RELATIONSHIP BETWEEN C4 AND H ILLUSTRATED WITH BELGIAN DATA (NACE-INDUSTRIES, 1981)
H
/
The figure
shows
the relationship between H and C4
in the
shape of a horn (*). A "horn" relationship is not only valid
for
C4,
but
applies
to
all
Ck
measures,
k
taking
on
different values.
The arguments that follow also hold for k
different
For C4
C42, which
the
from 4.
corresponds to the numerator of equation (3) for
collusive
boundary for C4
(*)
> 1/4, the upper boundary equals
outcome
<
with
four
leading
firms.
The
upper
l/4, equals C4/4 and can be interpreted as
The derivation of the boundaries follows from the
transfer principle, which the H-index satisfies, under
the restriction of given Ck values (see Sleuwaegen and
Dehandschutter (1985))
9
a
conditional
(upon
Adelman (1969)).
the
line
C4)
number
4
over
leading
should be
H
value
(see
Because of this relevance we have extended
the
whole
range
boundary of the horn is given by
all
equivalent
firms
noticed
hold
that
of
C~/4,
eqt!al
both
C4
values.
lower
or the H index when
shares
the
The
of
the
market.
It
upper boundary
1/4) and the lower boundary are the same for H4 and H since
the
maximum
and
minimum
H assume
the
remaining n-4 firms to approach zero.
boundary of H4
industries
is C4
2 •
displayed
Clearly,
in
figure
for
1
contribution
For C4
the
,C4
approximate linear relation to each other,
the
< l/4 the upper
sample
and
of
H
of Belgian
are
not
in
and hence are not
easily exchange~ble as explanatory variables
for pric~-cost
margins .
3.
Incentives to collude.
Recognizing that
the effect of collusion on industry profi-
tability depends
on the oligopolistic structure of the in-
dustry
this,
dition for
come
however,
involves
only one
collusive price leadership to emerge and to be-
effective.
Jesse Markham
In
(1951)
an
early
contribution
ditions are (i),
there
must
to
devised five different
collusive price leadership to come about
(ii)
prerequisite con-
the
subject
conditions
(1951).
for
These con-
the industry must be tightly oligopolistic,
be
effective
barriers
to
entry
in
the
10
industry,
(iii)
products are to be close substitutes,
demand must be relatively inelastic and (v)
(iv)
individual cost
curves must be sufficiently similar.
In two important comments,
O~tenfeld
(1952)
and Lanzillotti
(1957) argued that these conditions are not straightforward
to interpret.
ticularly
In the opinion of these authors,
restrictive
and at
the same
time,
they are parincomplete
in
their capacity of defining a unique set of equilibrium conditions for collusive price-leadership.
However,
without
criticisms,
exploit
spelling
out
all
the
details
of
these
it seems to us that the commenters did not fully
Markham's
interpretation
of
arguments
the
term
leading
to
"prerequisite
/the
right
conditions"
As
the real source of collusive arrangement Markham emphasized
the
of
each
individual firm and those of the industry as a whole".
It is
from
"identity
this
between
the
basic provision
long
that
term
the
interests
relevance
of the
five
more specific conditions should be interpreted.
The congruence of the individual firm's interests with those
of the industry will be closer the more concerted action in
the
indus try
argumentation,
does
result
these
in 1 arger
potential
benefits.
profits
In Markham's
constitute
the
hig-
hest incentive for firms to collude. Thus one should analyse
the significance of the five conditions
ship with these potential profits.
in their relation-
As we shall demonstrate,
11
formula
(3)
together with
Figure
1 provide
two
convenient
tools to do so.
The denominator of formula (3)
will
be
larger
(condition iv)
limit
lower
is
industry
and the higher
demand
are barriers
elasticity
to entry which
the magnitude of the competitive fringe supply elas-
ticity e
tion
the
implies that industry profits
(condition ii).
(iii)
product
is
poses
no
Also
the interpretation of condi-
particular
sufficiently
problems.
differentiated
When
from
the
firm's
rivals,
price
interdependence is low and the firm shapes its own industry.
The real controversy around Markham's conditions arose
conditions (i)
and (v):
from
the oligopolistic /structure and the
similarity of the cost curves of the firms in the industry.
Therefore,
the
analysis presented here may be most helpful
with respect to these two conditions.
Figure (1)
coopers t i ve
( Cournot)
low levels of concentration,
behaviour
corresponding
to
difference
formula
(3)
industry
it is only in
high Ck values,
returns
for
performance.
According
sentence
of
the
to
for
that collusion can yield these high industry
is
on
"can"
since
The emphasis
the
outcome
is
dependent upon the different positions of the firms.
shares
Hk-
makes
the wide zones of the horn,
compared to Cournot behaviour.
previous
non-
the
or collusive behaviour corresponding to Ck2,
index,
little
shows that for
large
firms
are
very
unequally
in
the
really
If the
distributed
...
12
resulting in a high value of the Hk
Cournot
or
collusive
behaviour
index within
would,
the horn,
following
formula
(3), make little difference in terms of industry returns.
some
particular
high
returns,
1 ike 1 y
to
collusion
zones
concentration
industry
most
cases,
may
in
even
collusion
that
provided
occur
concentration ratio to decrease (as
will be
the
In
very
decrease
makes
the
formally shown
in the next paragraph).
From Figure (1) we can derive,
however,
of negative
on
gins,
Hk
collusion effects
that the phenomenon
industry
price
cost
mar-
is only likely to occur in these industries with high
values for given Ck values.
row A (lowest Hk
index)
=H
This
~s
index possible)
illustrated with arand arrow B (high Hk
indicating the possible effects of collusion.
Case A
implies a very large increase in industry profits while for
case B, collusion would imply a decrease in industry profits
which
the
dominant
formally show
index
under
in
firm
the
Cournot
differentials
among
would
next
sect ion,
depends
the k
never
accept.
the
height
crucially upon
firms.
If
As
the
industrial
structures are similar the (Ck-conditional) Hk
we
shall
of the
efficiency
firms
cost
index will be
low and potential industry collusion rewards high. Thus,
with the degree of concentration,
Markham's
similar
original
cost
curves"
collusion
is
again
both figure (1) and formula (3).
Hk
as
the real meaning of Jesse
condition
of
analytically
"sufficiently
derivable
from
13
Formally,
the effect of going from Cournot to collusion can
be analyzed by differentiating
(3) with
to a.
respect
This
differentiation can be decomposed as follows
n
sA
= 6>.,
a-a.
Sa
As
+
~
!dsi=O
long as a
=1
i
the degree
6>.,
6Si
6Si
\da=O
of collusion,
( 4)
a-a
would not
sizes of firms within the industry (dsi
= 0),
affect
the
the effect of
increasing collusion would simply be:
> 0
Ck 2 - Hk
+ E(l-Ck)
-··-··-·----·--·-·-·--
Jl
However,
and E
and
>
( 5)
since collusive behaviour implies price increases,
Ck/ a is necessarily negative.
0,
in what directions
course depend
outcome
/
of
Hk
will
move with collusion will of
on what -firm wi 11
collusion
on
To what extent Ck
set which price.
industry
price
cost
The final
margin
will
depend on these concentration effects.
It
the
should
be noticed
concept
of
a
here
critical
that
the
results
concentrical
do
not
ratio
i.e.
lowest possible concentration ratio inducing firms,
of substantial possible profit gains)
However,
instead
of
considering
fixed magic number for
all
oppose
the
(because
to collude.
this
industries,
critical
it
ratio
follows
as
a
from the
14
analysis that the existence and magnitude of such-a ratio is
dependent
upon
other
structural
conditions
structure differences among firms and,
in
the
next
section,
the numbers
of
, such
as
cost
as will be discussed
leading
firms
in
the
industry.
The
increasing
Ck,
causing a to depend positively upon this last variable,
is
consistent
C 1 arke,
incentives
with
Davies
test our
some
to
collude
recent
and Waterson
Ck 2
larger values
empirical
( 1984)).
findings
However,
resulting
from
of
(see
to properly
a should be related
collusion hypothesis
difference between
for
collusion
to
the
and the
H
under Cournot behaviour./
4.
Industrial concentration under collusive
rice leadershi
~1:-~~opo!x
As Clarke
and Davies
gopoly model,
(1982)
have shown
for
the basic
oli-
the price leadership oligopoly model discussed
above implies a joint determination of both price-cost margin and concentration within the dominant group and the competitive fringe.
Following
their
analysis,
but
replacing
~
by
~o
(the
industry demand elasticity by the demand elasticity for the
15
k
leading
firms)
industry by
and n by k
the number
(the number
of firms
of leading firms),
it
in
follows
the
that
the truncated Herfindahl index for the leading firms equals:
H~c
=(
1 + rl
k
-
-
k(J..ID
.
a) 12 vc 2 )
.... k
l
C1t 2
(6)
J
where vc2 is the coefficient of variation of
in the group of leading firms.
fringe
are
firms
differences
will
price
reflect
marginal costs
Similarly, since competitive
takers,
it
efficiency
follows
that
differentials
size
or
not
exist if technologies are similar for fringe firms, with the
corresponding
characteristics
summarized
in
their
supply
elasticity. Accepting the last assumption, Hn-k, the H index
component for the fringe firms,
how Hn- k becomes very small
is easily computed and shows
for high values of Ck
or high
numbers of fringe firms.
n
Hn-
k
~ s
=
i
Since H
that,
= H~c
under
=It + l
i 2
+ Hn-k,
= i}. =:g~J~
it follows from the previous arguments
collusive
price
within the horn for a given
number
of
leading
( 7)
n-k
and
C~c
leadership,
the
H dispersion
value can be explained by the
fringe
firms
in
the
industry,
efficiency differentials and the degree of collusion amongst
the leading firms.
16
However,
the
leaves us with the problem of determiriing Ck,
this
joint market share held by the dominant
the marginal
cost
together with
functions
the market
and equilibrium
the
the market
Given
condition
demand constraint,
ciple possible to calculate
Hence,
k firms.
it
is
(2),
in prin-
share of each firm.
concentration ratios for both the dominant group and
competitive fringe
firms
can be calculated and related
to the set of parameters contained in these equations.
How-
ever,
cost
because
functions
of
involved may
clear
of
become
very
non-linear
fringe
tedious,
relationships.
To
form
firms,
and
are
proportional
firms
belonging
j=k+l, ... ,n,
to
the
to
not
and
competitive
this,
the dominant
we shall, adopt
group:
ciency difference
mci
= ao
given by
qi,
mcj
the
similar
i=l, ... ,
ratio
of
the
difference
between
the
k.
all
ac
qj,
=
(E
= 1).
for
Only an effi-
the
two
for
assumption
slopes
respective marginal cost functions 0 = ao/ac,
constitute
to
we shall
identical
fringe:
a
lead
that marginal
implying a unitary supply elasticity
convenience,
the
always
illustrate
output,
of
the mathematics
the most simple example and assume
costs
For
required
the competitive
explic~t
take here
the
of
the
is assumed to
groups.
In
ad-
dition to its analytical tractability this simple model with
cost equality among the leading firms has the
characterize the
most favourable
cost
advantage to
condition
for collu-
sive price leadership as discussed in the previous section.
17
This quality of the model enhances
the significance of the
results which will be obtained hereafter.
Under the assumptions made,
= P..L. .
,Ai
-
=
mCi
1 -
Pi
Summing Ai
=k
Ai
-
(n-k) .0.
(9)
is a
(8)
t~-~ ! . L! . . : . . . ~..!..J. . . g_~.t.
J.l + ( 1 - Ck )
good illustration of how
disadvantage variables
to
=
Ck
1 - Ck
i=l
Equality
= k+ 1, ..• , n
j
over all dominant firms yields:
k
~
lead to:
aCk + ... L~-----=---~~---~-.L
J.l + ( 1 - Ck )
=
':!.9L.
Cqj
= l, ... ,k
i
relations (1) and(2)
industry
price
between groups
cost
margins.
In
(marginal)
of firms
the
(9)
cost
are related
model
this
cost
disadvantage ratio plays a crucial role for the existence of
the dominant group. The continuous efforts of dominant firms
to
create
and
coupled to
benefits
to
take
the problem
with
background
for
connection
the
all
the
advantage
of enforcing
members
model
various
of
of
the
presented
arguments
these
differentials
collusion
and
industry
here
about
sharing
serves
(see
as
in
this
dominant
firm
behaviour offered by Geroski and Jacquemin (1984)).
Subtracting
the
members
each other we obtain
an
of
the
implicit
from which Ck can be solved.
last
equality
function
in
F(Ck,
(9)
k,
from
n,
0)
(With cost equality within both
18
groups
of firms,
From this
Hk
equals Ck 2 /k and Hn-k=
implicit function
follows
that
(l-Ck)2/(n-k)).
Ck
varies
in the
same way as (i) the degree of efficiency attained by the dominant
(ii)
(i)
firms versus fringe
firms
(inversely measured by 0)
the number of dominant firms;
the
degree
(fringe)
of
firms.
implicit
These
it varies inversely with
collusion,
effects
follow
(ii)
the
from
the
number
of
following
differentiations of (9):
Defining F'ck = 8F
8Ck
-
(n-k) .0.
=
-·····-··--J.P.............~......!) ··-········ .
1
(l-Ck)2
[ k a + ( 1- a ) ] < 0
(ll + (1-Ck) )2
it follows
(n-k)<:;!r.
1-Ck
F'ck
-1 +
8Ck
=
aCk
Bk
8Ck =
Bn
(10)
0
• • • • • • • • • • • • • >< . . . . . . . . . . . . . . . . . . . . . . . . . .
1-1
0
<
-~-.....L~.:.S:.~:r.J....
F'ck
Ck
1 - Ck
F'ck
······-·-···--·····.. ·····
. >o
if (a+l)Ck
<
<
>
IJ.+l
(11)
< 0
( 12)
(k- 1) Ck
8ck
Ba
= -·-·1:!:...~.. -J !.... : . . g_lc)
rivations is
the
(13)
0
F'ck
For the aim of this paper,
of
<
k
the interesting result of the de-
the negative effect of a
largest
firms
in
(13).
It
on the concentration
implies
the
more
19
perfect collusion
is,
the smaller will be market share held
by the dominant firms
in the industry.
follows
(given
broad
meters)
that
behaviour
some
the
will
assumptions
effect
on
larger
the
be
From equation (13)
Ck
about
of
other
increased
greater
k:
the
it
para-
collusive
number
of
leading firms.
However,
to evaluate this
industry profitability,
k
values
change Ck,
corresponding
Ck2/k).
It
according
the
to
be
the
in connection with
~erified
it should be
concentration
(minimum)
may
latter effect
how increasing
ratio
and
Hirschman-Herfindahl
inspected
sign
that
condition
for
in
Hk,
index
low
( Hk
values
formula
the
of
(11)
=
a,
these
/
effects
do
increase
potential
effects of enlarging k,
in
the
concentration
illustrated
index
in
corresponding
with the
equal
2.
for
The
the
to zero,
the larger is k,
the
shape
values
"equal
lower boundary of the
for larger k values.
a
to
benefits.
The
the number of leading firms included
ratio,
Figure
collusion
of
cost"
of
the
the
horn
is
truncated
Hk
ex amp 1 e
coincide
hornr which shift downwards
Thus, for all given Ck values and with
the profit
co 11 us ion potential
is 1 ar ger,
the number of leading companies.
A further illustration of these effects can be obtained from
numerically solving formula (9)
for different values of k
20
FIGURE 2
ILLUSTRATIVE MODEL WITH INCREASING COLLUSION
H
I
..:.·~£
-1 -
;
- I
0.8 -i
I
I
' - i
\./_"1
l
o_e
-j
''
I
.- c
'
V--'-:
''
l
0.4 -t
I
0.~
i
-4
I
Q.: ~
'
0.4
and a.
This
increasing
firms.
yields
C.E
the following
collusion
with
illustrative
different
results
numbers
of
for
leading
The concentration effects are indicated by arrows
in
Figure 2 while full results are reported in Table 1.
TABLE 1. NUMERICAL RESULTS FOR THE ILLUSTRATIVE MODEL
Ai
k
a
a
a
=0
= 0.5
=1
=4
k
Ck
=
10
k
=4
Hk
k
=
10
=4
k
k
=
10
.114
.113
.405
.689
.041
.047
.246
.445
.367
.581
.034
.034
.347
.611
.344
.493
.030
.024
(Other parameters values were ll
= 0.30,
n
= 30,
0
= 0.20)
21
From Table 1 we may inspect that the gains from collusion
are highest for the group with ten leading firms which show
the highest increase in individual price-cost margins but
also the steepest decrease in concentration. These movements
are reflected in both the length and inclination of the arrows drawn in Figure 2.
5.
Summar
The
and Conclusion
present
paper
analyzed
the
effects
of
going
from
non-
cooperative Cournot behaviour to collusive behaviour within
/
a
group of leading firms
a
fringe
of
firms
in
an industry that also includes
acting, as
price
takers.
The
study
confirmed the relevance of Jesse Markham's collusion conditions by formally showing how differences
fit
mar gins
under
co ll us ion
increase following the height
versus
Df
in industry proCournot
behaviour
the concentration ratio of
the k leading firms and the similarity of their cost curves.
These
differences were
analyzed within the framework of an
existing horn shaped relationship between the concentration
ratio and the Hirschman-Herfindahl index. As potential gains
from collusion,
the industry profit margin differences were
interpreted
constitute
dominant
to
firms
to
collude.
the
By
strongtest
linking up
incentives
the
the concept of a critical concentration ratio,
results
for
with
the analysis
22
was
able
to give some more
Finally,
within
it
the
was
shown
group
how
contents to
increasing
leading
of
the latter concept.
collusive
firms
behaviour
leads
to
lower
concentration ratios in the industry.
The analysis
clearly pointed out
of considering more than
the
observation.
useful
empirical
This
results
It would be
consequences
research
for
theoretical
relevance
just one concentration measure
assessing industry performance.
know
the
would
anti-trust
of
interesting to
this
theoretical
undoubtedly
policy.
in
In
yield
the
some
merger
guidelines recently issued by the U.S. Department of Justice
the
choice
of
concentration
measure
as
preliminary
indicator of market power showed up as an important matter.
23
6. References
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M.A.,
1969,
Comment on
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de
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24
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