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Onder:oeksrapport Nr.
8601
THE HERFINDAHL INDEX AND CONCENTRATION RATIOS REVISITED
By
Leo E.
Sleuwaegen, Raymond R. De Bondt and Wim V.
Dehandschutte<
Feb ~- u a ~- y l 9 8 6
Revised May 1986
t·Jette:iJk
depot
D/1986/23'/~_S/2~
THE HERFINDAHL INDEX AND CONCENTRATION RATIOS REVISITED.
By
Leo E.
Sleuwaegen,
Wim V.
Raymond R.
De Bondt and
Dehandschutter.
Introduction
One issue of long standing in both economics
organisation)
and
and
workable
measurement
intrinsically
cause
it
is
behavioral
in
difficult
related
vial problems
these
to
arise
practice,
market
concerns
power.
empirically
the
Market
grasp,
structural
correct
power
if
is
only
be-
(concentration)
and
characteristics of the industry which
related to
some attributes
•
of
to both
(collusion)
turn may be
ficiency 1
antitrust
(industrial
each other.
In
addition,
if market power measures
of economic welfare,
such as
nontri-
are related
to
allocative ef-
Notwithstanding a continuing debate on aspects of
issues
(in
the
field of
titrust laws are applied,
industrial
organisation)
an-
relying among other things on mea-
sures of concentration .
......................
1 Cf. efficiency vs. market power controversy. See e.g.
Demsetz. Two systems of belief about monopoly, in
Goldschmid, Mann and Weston (Eds.), Industrial
concentration, the new learning, Boston;··r::rtt.ie & Brown,
(I974Y·:··Is4=I·s4; ··c;-ya:·rke·:· Davies and waters 0 n The
profitability-concentration relation: markey power or
efficiency?,
3 2 ' 4 3 5 - 4 50 . The
• • Journal of Industrial Economics, (1984),
j
0
n
•
•
•••••••••• ••••••••••••••••••
•
no
0
0
•
••
•
•
••
•••••••••••••
••
-•n
•
r..:,.
The 1982 and 1984 modifications of the Justice
include a shift
ment's merger guidelines2
and
intuitively "clear"
four-firm
depart-
from the
concentration
simple
ratio
(C4)
that equals the total market share of the four largest suppliers,
to
the
somewhat more
(or Herfindahl-Hirschman)
rage
of
all
of
the
sophisticated Herfindahl
(H)
index that equals a weighted ave-
"revelant"
firms'
market
shares,
with
each market share given a weight equal to its own value.
From a practical
point of view it
would appear worth-
wile to have a clear, operationally useful, understanding of
the
H index
of concentration.
A number
of authors
already
made important progress towards "explaining" the H index, by
relating
it
mathematical
numerical
Through
to
manipulation
it
has
been
examples
shown
and
that
no
guarantee exists for a one to one relationship between the H
and C4
indices.
Two
industries with different market
distributions can have the same H value.
number
appears
typically will
useful
characteristics
to
correspond a
report
and
relation between the
in
this
implications
Ck
And with a given H
range
of C4
paper more
of
share
the
values.
fully
on
It
the
correspondence
(k firm concentration ratio) and the
2 See, for example Bronsteen, A review of the revised
Mar ger Guidelines, 'T...l:l~ .. ~~~t~E~.'?.~ ... ~~ll~~~.~ ( 1984) , 2 9,
613-652.
3 For this Journal, see Weinstock, Using the Herfindahl
Index to measure concentration, The Antitrust Bulletin
(1982), 27, 285-3ol; Miller, The--He. r"flnd:ahi·=-!IIrsc"hma!1-·
Index as a market structure variable: an exposition for
antitrust practitioners, The Antitrust Bulletin (1982),
2 7' 5 93-618; Weinstock' s"()"ffi"e"""""TTt"""Fie"=kn"ow"ii"""""P""r""(j"i)e rt i es 0 f
the Herfindahl-Hirschman Index: problems of translation
and specification, 'T...~.~·-····~·~·~·~ . ~rust Bulle.. tt~. ( 1984), 29,
705-717.
H index.
ship
has revealed a h<?.E. r.?. shaped relation-
Data analysis
between
several
the
index
H
characteristics
and
that
concentration
can
ratios,
with
contribute
to
a
better
boundaries
of
the
understanding of these measures.
In
the
following
section
the
correspondence
are
and U.S.
The relevance for
data.
discussed
and
illustrated
with
Ck-H
Belgian
interpreting and valuating
H values and for assessing economic performance is discussed
next
after
which
the
relation
with
the
U.S.
Department
of
Justice's merger guidelines is clarified.
Relating the Herfindahl index to concentration ratios.
Suppose that
and that
firms
a
are
relevant
ranke~
industry is
according to
served by .n
their
of sales, with the largest firm being firm l.
size
firms,
in
terms
The Herfindahl
index of concentration H is
n
H
=~
Si 2
with
Si
denoting
the market
share of
the
i= l
i-th largest firm.
It can be verified that 0 S H S l
H
=
and
l/n + cr 2 n
with cr2 equalling the variance in the market shares,
i.e
n
(l/n) [
~
(Si
-
l/n) 2
].
All firms having equal market share
i=l
means that cr 2
=0
and then H
=
l/n.
The
k
firm
concentration
ratios
Ck,
k=l,2,3,4, ...
sentially give no weight to the market share of firms
For
example,
indicate
=
C2
+
s1
respectively
s2
the
and
=
C4
two-
and
s1
+
+
s2
four-firm
es-
>
j
+
S3
k.
S4,
concentration
ratio.
Both the Ck
share
distribution
surprising
clear,
in
that
they
however,
that
functional
(one
from partial
while
and H indices are a reflection of the market
the
the
somehow
in
to one)
index
are
general
and
hence
related.
there
takes
the size
the
it
does
not
is
not
it
is
exist
a
calculated
distribution
complete
is
Likewise
relation since the Ck
information on
H
industry
of
firms
distribution
into
account.
Using
the
distributions it
that
contains
extreme
is
all
possibilities
nevertheless
possible
of
market
possible to define a
H values
for
given
Ck
share
range
values 4
This Ck-H range turns out to have the shape of a tl..?.E. ~.'
•
since
the range of possible H values increases as the magnitude of
Ck
(for
a
given
correspondence
is
k)
becomes
dependent
on
larger.
both
The
the number
horn
shaped
of firms
4 Or all possible Ck values for given H magnitudes.
in
the industry
(n)
and on the number of firms
(k)
included in
the Ck computations.
For a "large" number of firms in the industry
speaking for n
~
oo)
relatively simple,
the boundaries
of the H-Ck
(strictly
relation are
i.e.
H
0.9
0.8
0.7
0.6
~
I
0.5l
I
0.4
I
0.3
X
0.2
0.1
0 0
0
Fig.l.
The
0.2
horn
shaped
0.4
0.6
boundaries
0.8
for
the
C4-H
relation
5 In general for n firms and a Ck ratio, which cannot be
smaller than k/n, the boundaries are for n > k, min H =
Ck 2 /k + (l-Ck) 2 /(n-k); max H =max {[1-(n-l)(l-Ck)/(n
-k)J2 + (n-1) [(1-Ck)/(n-k)]Z, Ck/k}, except for a
fraction if the maximum is Ck/k and k(l-Ck)/Ck is non
-integer. A proof is given elsewhere, see Sleuwaegen and
Dehandschutter, The critical choice between the
concentration ration and the H index in assessing
industry performance, forthcoming in The .J:. ?..~.E..l?.'?:. ~ .....<?...f
~-.l?. 9.:..L.1:.:5...!..E...~.~}-.... Xs:<?..!:l?.I_ll:.~.<?.. ::> , C 19 8 6 ) .
min H = Ck 2 /4
and
for
max H = Ck/k
for Ck:Sl/k
except for a
is not an integer number.
This mathematical
fraction
range
if k/Ck
turns
out
number of firms
few
firms
n~ro,
Ck~l/k
max H = Ck 2
say
n=l5,
not
to
in the
n=lO,
very
industry,
:s: n
15
be
:S
4.
sensitive
except
This
is
n=5 in the H-C4
to
the
if there
actual
are only a
illustrated
for
diagram of fig.
k
= 4,
1.
The boundaries of the horn shaped correspondence shown
1 define
in Fig.
observed,
given
for
C4
the range
because
of
purely
concentration
given
industries
may
firms
but
it
any
boundaries
case
mathematical
ratio.
with the number of
in
of possible H values
change,
actual
say
or with the
will
corresponding
The
always
to
a
large
reasons,
with
a
H and
C4
pattern
year
to
year
from
level
lie
that can be
or
of aggregation,
within
number
of
the
horn
firms.
For
some cross sections the relation between the actual H and C4
values
may
whatsoever
be
approximately
exists
for
this
linear,
to
be
the
but
no
typical
case.
point is well underscored by Fig.
2 and 3.
pattern for
clearly widened
to
1981.-
3 digit
The
nevertheless,
NACE
more
sectors
disperse
as it should,
horn
less
relation
clear
revealing
between
now,
is
an
and
the
C4
would
and
artifact
This
The Belgian horn
pattern
in
from
1981
1975
stayed
within the boundaries indicated.
Published data for the U.S.
are
guarantee
3 digit sectors
appear
H values.
of
the
to
(see Fig.
suggest
This,
limited
it
data
a
linear
should
set
4)
be
which
H
0.9
0.8
0.7
0
0.6
0.5
Dll
0 0
0
0
0.4
0
,0
0
0
0.3
0
X
0.2
0.1
0
0 0
Fig. 2.
0.2
The
horn
0.4
relationship
0.6
for
(source: unpublished statistics
Statistical Institute).
0.8
Belgian
from
industries
the
Belgian
(1975)
National
H
0.9
0.8
0.7
0
0.6
0
I
0
o
0.5
o o
0
m
0
0.4
0
0
0.3
0
X
0.2
0. t
0
0
0
Fig.
3.
0.2
0.4
0.6
0.8
The horn relationship for Belgian industries (1981)
(source: unpublished statistics
Statistical Institute)
from
the
Belgian
National
H
0.9
0.8
0.7
0.6
0.5
0.4
0
03l
X
0.2
0. 1 -1
0
Fig.
I
o
0
0.2
4.
0.4
0.6
0.8
The horn relationship for U.S.
(source:
Nelson,
R.L.
Manufacturing Industries
Yale Univ. Press)
industries
(1956)
(1963),
Concentration
in
the
of the United States, New Haven,
H
I
1
0.9
J
::jI
I
o.s
0.51I
0.4 1
O.J
lI
0.2
-i
0.1
J
0~~~~~~=-----~----~---0
Fig.
5.:
0.2
0.-/.
0.8
0.6
The horn boundaries for k
=
l,
2,
Ck
4 and n->cn
s tops
at
reasons)
= .87
C4
( pres um a b l y
because
of
con f i dent i a l i t y
6 •
The horn shaped correspondences between H and other Ck
ratio's follow a pattern that is illustrated by Fig.
figure indicates
relationships
Within
small
the boundaries
in
industries
with
the corresponding set
number
of
firms
in
for the H-Cl,
large
number
of boundaries
the
illustrated earlier in Fig.
a
industry
H-C2
the
5.
This
and H-C4
of
firms.
range for
follows
the
a
pattern
1.
Interpreting H and Ck values
The horn shaped boundaries reveal some regularities than
can be further interpreted.
number of firms
origin
(OX
possible
in
The horn boundaries for a finite
all have their origin at a
Fig.
levels
of
l).
H
This
and
Ck
line
represents
that
can
be
industry with a number of firms equal to n
To see this,
nations,
the
note that,
line
which H = C<t/4.
OX
line through
for
The corresponding
all
H
minimum
observed
=
example for
represents
the
and
l/H
=
concentration
in
an
k/Ck.
the H-C4
C<t
the
combi-
values
for
levels
all
6 A referee pointed out that unpublished material prepared
by the U.S. Department of Justice contains similar horn
shaped correspondence for U.S. industries. The
investigation of the boundaries and their implications,
however, appears to have not been explored previously.
1U
have the same numbers
equivalent.
The numbers
equivalent
ne
is the number of equally sized firms that corresponds with a
given concentration measure value.
number of firms
For
that given concentration measure value.
the
example,
=
satisfies 0.2
numbers
for
numbers
l/neH
e qui valent
It is the lowest possible
equivalent
=
4 I C4
=
0.2
0.4
the
H
for
= 5, while for C4 =
= l 0 . In general n e H
or neH
ne c
neH
and n e c
solve:
H
=
1/neH and
=
C4
4/nec
Those values of H and C4
for which the ne
values are equal,
satisfy
When
n urn b e r s
the
actual
e q u i v a l en t ,
number
t hen
of
t he
firms
equals
mark e t
is
the
calculated
e qua 11 y
di s t r i but ed
and consequently the concentration is minimal for that given
n.
Both for
industries
below the
values
the
are
line
U.S.
and Belgium
characterized
H
=
C4/4
by
(below
corresponding with a
C4
the
and
C4
OX
majority
values
H
in Fig.
lower
than
of
2,
or
3
3
digit
that
lie
and 4).
equal
H
to C4/4
can be considered "low" while H values larger
than the C4/4
value
judged
"high".
of
the
Indeed,
industry
can
<
C4 /4
if H
intuitively
it means
that
be
~--~.Y...:=.. I.?.
to
be
the market
L
share of the four
firms
in
the
largest firms,
industry
is
not
the inequality between
very
large
as
the
the
following
example illustrates.
Sl
S2
S3
S4
ss
S6
S7
sa
Sg
SlO
C4
H
cr2
.28
.20
.19
.13
.07
.04
.03
.02
.02
.02
. 80
.18
.008
.34
.21
.14
.11
.07
.04
.03
.02
.02
.02
.80
.20
.010
.80
')-
.015
.44
.11
.16
More
value (1/n
is
however
not
(0.80/4).
have
a
also
with
a
H
C4
precisely because
small
will
only if
the
10
an
this
firm
is
·~!)
clear
is
larger
than
that
a
its minimum
firms in the industry have
The
inequality between
the
the
share of 0.80,
precise
sense
industry with a
=
0 . 20 .
Now
t here
=
0.80
and
unequal
there
:L. . .~.~. sl:.......?.. ~...!X...-...~...f
.~ .
it
firms having a
in
firm
is
the larger number
0. 2 0.
0).
.01
.01
that
the
is not able to tilt the H value above
)
A five
mi n i mum
>
large
positive variance (a 2
0.20
0.18
largest
very
10
hence,
(cr 2
with the four
shares
=
of H
shares
=
n
= l/10 = 0.10),
unequal market
firms,
if
precisely,
concentration level
.055 .025 .02
.08
.09
a
small
of firms
in
n
variance
is
industry
with
C4
10
0.80
shares
H value
be
= a2-ljn 2
the
the
market
is
and
very
if
H index
larger
•
But
H value below
minimum H index in the 5 firm industry with C4
7 The reasoning is based on dH/dn
shares.
in
the
enough will
=
0.80 would
f i r m indus t r y
variance
the
=
market
in market
lower
large
a
lowers
the variance
increase
is
C4
than
= 0.80 7 .
and
ln
the
Calculating H values from Ck
The
horn
values
correspondences
from
a
1 imi ted
also
allow
knowledge
of
the H index somehow gives
picture of the
industry,
market shares,
of
possible
industry
could
H values
that
can
very
low
(see
Fig.
if
you
know
the
firms,
you
don't
need
the possible H values
•
The
"complete"
into account
C2
values
Somewhat
market
to
H
all
The spread for example
accompany
5) 8
shares.
a more
takes
needs to be qualified.
state:
largest
since
is
it
calculate
market
intuition that
because
to
shares
know
lie within a
the
in
an
crudely
one
of
two
other
the
shares,
narrow bound that
can be calculated.
The range of possible H values
that can accompany Ck
is
dependent on k and this can be explored to approximate H.
If
one is
interested in obtaining the H index for a particular
industry
and
allows
for
a
maximum
error
of
1
percent,
it
8 The maximum spread of possible H values is
6. s; max
H(n~ro) - min H(n~ro) with max H(n~ro) and min H(n4ro)
defined on p. 5. For Ck < 1/n
6. s; Ck/k - Ck2
approximately. This range increases as k gets large~ but
is small for k = 2 anyway. For Ck ~ k, k ~ 2, 6. s ((k
-1)/k) Ck 2 and the maximum spread of H values is minimal
for k = 2!
.,
........'·
/
suffices
to
sum
the
squares
of
the
k
largest
amount HR given by the following expression 9
HR = 0.5 [(1-Ck)
where,
as before,
Ck
(Sk
=
Sl
firms
and
an
.
+ (1-Ck)/(n-k)]
+ S2 + ... + Sk.
The number of firms k required in the computation is
implicitly given by the condition:
Sk(l-Ck) -
HR
~
(*)
0.01
This implies that in many cases the need for information
on market shares may be very small making the computation of
H indices
very easy.
For example,
of 50 firms but where
0.07,
ss
.... '
=
approximation
account
of
Sl
H
the
=
0.40,
=
ss 0
shares
= 0.30,
s2
To
H-index
only the market
9 The H index,
=
take an industry composed
obtain
it
an
suffices
of the
three
S3
=
0.10,
almost
to
=
perfect
take
largest
S4
into
firms.
n
~
Si 2 , can be written asH= Hk + Hn-k,
i=l
k
where Hk
~
=
n
Si2 and Hn-k
=
~
S l. 2
•
If Sk (the market
i=l
i=k+l
share of the k largest firm) is known, straightforward
application of the transfer-principle (see Hannah and
Kay, p. 22) implies:
max Hn-k = (1-Ck)Sk + (~ 2 - ~)Sk 2 , where~ is the
fraction implied by the division in the first term.
Similarly, min Hn-k = (l-Ck) 2 /(n-k).
The possible spread of H values is max Hn-k - min Hn-k.
The midpoint is (max Hn-k +min Hn-k)/2.
The condition
(*) ignores the small fraction ~ and takes a 0.01 %
deviation upwards and downwards from this midpoint.
Hannah and Kay, Concentration in modern industry, Theory,
Me as u rem en t and f"h'e'"'""'u'K"""'""ifx"i~e·:r···_ce·nc·e·:--·---L·oiidon·;··---·T}i:"e"'''Ma"c"M:C'Cian"'
. 7··y--:--···--······--·-···--·--···--···--·--·----·······-----······--·-····--··----· . . . . . . .
F'·:r·e·s-·s--·~····----·ri·ff7
Using the method outlined above,
computing HR
fo~
the
three
largest firms yields:
= 1/2
HR
[(1-0.80)(0.10 + 0.004)] = 0.0104
implying that the precision condition is met:
~
(l-0.8)0.1- HR
0.01
The corresponding H index approximately equals:
H
= (0.4) 2
+ (0.3) 2 + (0.1)2 + 0.0104
= 0.2704
The horn correspondence and economic performance
Assessment of possible welfare
losses in an
industry on
the basis of one concentration measure may be misleading,
view
of
the
horn
correspondence
and
established
in
economic
theory.
Static misallocations and excess profits because of
market
power,
increases,
will
even
independentlylo.
industry with a
tend
the
if
This
low
to
does
be
larger
firms
in
not
mean,
H necessarily will
as
the
the
H
index
industry
however,
act
that
be accompanied
an
with
10 See Dansby and Willig, Industry Performance Gradient
Indexes , A.I.Il.~.E-~~?.:.~......~.~-g~_g_f.ll..~.~----~~.Y..~~-~-, (June 19 7 9) , 6 9, 2 4 9
-260.
small
with
welfare
a
losses 1
higher
C4
1
and
Indeed
if
the
a
low H
leading
~. t:l..X.
be
four
accompanied
firms
were
collude, excess profits will tend to be high as welll2.
low H were to be accompanied with a low C4
to
If a
(Ck) there would
be no need to look beyond H.
To
achieve
an
operational
interpretation
of
values
H
without reference or knowledge of the C4 1 the several regions
of
the
horn
correspondence
can
be
helpful
to
achieve
guidelines for antitrust analysis.
The U.S. Department of Justice's new merger guidelines
One of
the most
noted modifications
that
resulted
from
the 1982 revision of the merger guidelines was the adoption
of the H index instead of the four-firm concentration ratio
as a first
The
indicator of possible exercise of market
primary
that
the
H
distribution
argument
index
for
reflects
firm
of
this
change
better
sizes
in
was
the
C4
power.
observation
than
the
the
the
industry.
actual
Another
important argument brought forward by the Justice Department
'"''""''''
>••>••••o•o•••••••••-<n•><
''''''''''''''""'''''''''''''''''''''''-''''''''""'-'''''
''''''"'''
ll As would be suggested, for example, by the contribution
o f S t i g 1 e r , A t he or y o f o 1 i gop o l y , !.. <?...~E_f.l.t:i.. .l::.......?...f.... ~. 9.._1...~..!.~. <?. a l
~.£g.~. 9...~X· (Febr. 1964), 72.
12 See also Clarke, Davies and Waterson,
opus. cit. and
Sleuwaegen, On the nature and significance of collusive
price-leadership, International Journal of Industrial
.. . §.l.. . .
.9..!::_g_~-~ ~
~.! ~.g-~_,
c19 s6")··-;. . . . 4. . . . .(.Iii . . . .P'.r"e's"s'}·:··. ··--.. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
is
the
greater
decision
predictability
rules
concerning
of
its
whether
or
merger are clearly specified in terms
index and the
decisions
not
to
since
the
challenge
a
of the post merger H-
resulting increase of the H-index.
The
report
states :
The
Department
divides
the
spectrum of market
concentration as measured by the HHI into three regions
that can be broadly characterised as unconcentrated
(HHI below 1000), moderately concentrated (HHI between
1000 and 1800)
and
highly concentrated (HHI above
1800). An empirical study by the Department of the size
dispersion of firms within markets indicates that the
critical HHI thresholds at 1000 and 1800 correspond
roughly to four-firm concentration ratios of 50 ~~ and
70 %,
respectively.
Although the
resulting regions
provide
a
useful
format
for
merger
analysis,
the
n um e r i cal d i v is ions s u g g e s t great e r pre c is i on than is
possible
with
the
available
economic
tools
and
information. Other things being equal, cases falling
just
above
and
just
below
a
threshold
present
comparable competitive concerns".
the
Comments
on
H-index
has
industry
when
changes
have
probusiness
to
using
argued
benefit
the
C4
ratio
the
H-index
that
a
is
the
use
of
non-competitive
classified
more
the
more
the
largest
does
not,
contrary
shares are equall3.
This
common
a
according
competitive
firms'
these
division
of
the
interpretation,
non-change
of
indicates
the
the
spectrum
necessaril
guidelines
"winners"
considered less concentrated,
"loserstt
(the
more
·································-·······-···-···········-··························-··"·······
-
in
imply
judging
(those
a
loosening
mergers.
industries
to
or
a
Figure
6
which
are
the dotted line zones) and the
concentrated,
the
dashed
line
13 See, for example, A Loosening of Merger Rules,
Week, (May 17, 1982).
zones)
Business
1·.:.:.::
resulting from the switch
index
thresholds.
industries
tresholds,
defined
from C4
Comparing
according
thresholds
the
to
the
to
highly
C4
or
the
new H-
concentrated
the
H
upper
it should indeed be observed that the
H
0.9
0.8
0.7
0.6
0.5
0.4
0.3
0.2
0. f
C4
0
0.2
0
Fig.
0.4
0.6
0.8
6
The horn relationship and the tresholds of the
Justice Dept. for both the C4 (1968 guidelines) and the
H index (1982 guidelines) illustrated with U.S.
1956
data (Nelson (1963)).
actual (1958
number of
VS)
losers.
distribution of firms
But as distributions
necessarily be the case (anymore).
would imply a
larger
change this need not
JC:
However,
in view of
measures,
concentration
and
the new evidence
tresholds
constitutes
treshold
clearly
some
adoption
the
progress.
delineates
characterized by high H index,
a
on welfare
The
H-index
upper
region
as well
of
of
as
losses
H
index
industries
high Ck
values,
related under either collusive or non-collusive behaviour to
unwanted possible allocative inefficiencies.
Conclusions
There
between
exists
the
a
horn
Herfindahl
shaped
index
and
correspondence
the
k
firm
relation
concentration
ratios that allows to :
in
an
define the range
industry
with
of possible H values
given
Ck
ratios
(or
that
can exist
alternatively
the
range of possible Ck'S with a given H);
-interpret better changes in Hand Ck,
H values
may
be
equated
with
magnitudes
since high (low)
larger
(smaller)
than Ck/k;
-
possibly approximate the range of possible H values if
partial
observation
are available;
on
say
market
shares
of
leading
firms
-
interpret
the new merger guidelines,
the horn shaped correspondence do not,
"loosening"
in
line
of merger policy,
with
recent
evidence
but
on
are,
the
which
in view of
in principle, mean a
better than
before,
relationship
between
welfare losses and structural concentration measures.
The
discussion
suggested that
the
focus
on
in
H.
of
fact
Given
the
horn
shaped
correspondence
it may make little sense to
existing
insights
on
restrict
welfare
losses
associated with either collusion or independent behavior,
makes sense to relate H to the corresponding C4.
boundaries employed in
the new merger guidelines
appear to do precisely this.
In fact
it
the
implicitly