We analyze the competition between two newspapers in a vertical differentiation model where the qualities of the journals are determined endogenously in the first stage of the game. We show that when the advertising revenues per reader increase there is a critical value above which the quality of the low quality newspaper discontinuously falls while it become similtaneously a free newspaper. This is beneficial to the high quality journal and detrimental to the readers.Advertising, Newspaper quality

Didier, LAUSSEL

Jean J. , GABSZEWICZ

Nathalie, SONNAC

English

Research Papers in Economics

Département des Sciences Économiques
de l'Université catholique de Louvain
Advertising and the rise of the free daily 
J.J. Gabszewicz, D. Laussel and N. Sonnac
Discussion  Paper   2006-45CORE Discussion Paper 2006/87
Advertising and the rise of the free daily
newspapers
Jean J. Gabszewicz
CORE, Université Catholique de Louvain
Didier Laussel
GREQAM, Aix-Marseille Université
Nathalie Sonnac
CREST-LEI, Université de Paris 2
October 12, 2006
Abstract
We analyze the competition between two newspapers in a vertical dif-
ferentiation model where the qualities of the journals are determined en-
dogenously in the ﬁrst stage of the game. We show that when the adver-
tising revenues per reader increase there is a critical value above which
the quality of the low quality newspaper discontinuously falls while it
becomes similtaneously a free newspaper. This is beneﬁcial to the high
quality journal and detrimental to the readers.
JEL Classiﬁcation: L150, L820
Keywords: Advertising, Newspapers quality
11 Introduction
In this paper we provide a theoretical explanation for the uprise of the free
newspapers’ press which is based on the expansion of advertising revenues. A
now large and bulking literature has analyzed the inﬂuence of growing adver-
tising revenues on media content and, more speciﬁcally, on newspapers’ content
(see for instance Anderson and Coate (2006), Gabszewicz, Laussel and Sonnac
((2001), (2002), Dukes and Gal-Or (2003)). However there is another remark-
able, though rather new1, feature in the development of the daily press industry,
namely the emerging uprise of several free newspapers (such as "Metro" or "20
minutes" in eleven European countries). Presently, free daily newspapers ex-
ist in 38 countries and 23 million copies are read by at least 45 million people
daily. In spite of this impressive uprise, traditional no free newspapers still
do cohabit with the press which is sold for free. To the best of our knowledge,
these features have not yet attracted the attention of theoretical scholars. In
particular, no analysis seems available so far which would provide an explana-
tion for the development of free newspapers, as well as the simultaneous survival
of the traditional daily press. In this note we provide a tentative explanation
of this phenomena which is based on the idea that traditional newspapers are
perceived by the readership as being of higher quality than those aﬀorded by
the daily press distributed for free to the readers. It is of course diﬃcult to
deﬁne an objective criterion in order to rank daily newspapers by their intrinsic
quality. Furthermore, newspapers’ characteristics are so numerous that re-
ducing quality to a one-dimensional criterion seems hazardous. Moreover, daily
newspapers are generally horizontally diﬀerentiated according to their position
in the political spectrum. Nonetheless, it seems a reasonable approximation to
assume that all readers would consider that free and no free daily newspapers
can be qualitatively ranked, the latter being of higher quality than the former.
The advantage of this simpliﬁcation is that it allows us to analyze competition
between traditional and free newspapers in a standard simple vertical diﬀerenti-
ation two-stage game2 in which advertising revenues are taken into account, and
in which newspapers’ editors choose the quality levels of their outlet. However,
contrary to several recent papers, in which the advertising market is explicitly
described and the revenue per reader endogenously determined, we view here
the advertising revenues per reader as exogenously given. Here we derive the
game equilibrium as a function of the advertising revenues per reader. Our main
ﬁnding is that, when advertising revenues expand beyond some level, the low-
quality newspaper’s editor decides a sudden drop both in the quality level of his
outlet and of its price: he starts to provide it for free to the readership! This
gives an endogenous explanation for the existence of free newspapers. Moreover,
in spite of this apparently predatory behavior, the low quality editor does not
evict at equilibrium his rival who sells the traditional newspaper at a positive
1In France the phenomenon appeared in 2002.
2see for instance Gabszewicz and Thisse (1979).
2price. On the contrary, in our model, this leads to an increase in the total
revenue of the latter !
2 The Model
We assume that there are two competing newspapers i = 1,2, which operate
in two interrelated markets: the readers’ and the advertisers’ markets. In the
readers’ market they diﬀer only by their qualities q1 and q2, qi ∈ [0,1], and
their prices p1 and p2. In our interpretation newspaper 1 corresponds to the
"traditional" newspaper. We assume the readership is neutral with respect to
advertising3. They diﬀer in their degree θ of preference intensity for quality.
A typical type θ-reader derives a surplus θq − p from buying at price p a
newspaper of quality q and a surplus 0 when refraining to read any newspaper4.
Under our assumptions readers single-home: they never buy the two newspapers
simultaneously. Given readers’ ad-neutrality, we may suppose without loss of
generality that each newspaper derives a constant proﬁt s per reader from selling
ads to advertisers5.
We consider a two-stage game in which the newspapers’ editors ﬁrst choose
their qualities and then their prices. Assuming that q1 > q2, demands Di,
i = 1,2, to the ﬁrms obtain as
D1(p1,p2,q1,q2) = 1 −
p1 − p2
q1 − q2
;
D2(p1,p2,q1,q2) =
p1 − p2
q1 − q2
−
p2
q2
;
and, assuming a zero marginal cost, the second-stage proﬁts πi are given by
π1 =
￿
1 −
p1 − p2
q1 − q2
￿
(p1 + s);
π2 =
￿
p1 − p2
q1 − q2
−
p2
q2
￿
(p2 + s).
3On this point see Kaiser (2006).
4When the quality q2 of newspaper 2 and its price p2 are simultaneously equal to 0 the
utility of buying newspaper 2 is equal to the utility of the outside option which is itself equal
to 0. In this case we assume that readers opt for getting newspaper 2. This speciﬁcation has
some importance because it corresponds to the case of a free newspaper of minimum quality.
An alternative formulation of the model would consist in setting the minimum quality at a
strictly positive level. However it considerably complicates the algebraic treatment of the
model without providing any further insight.
5Since readers single-home each newspaper acts as a monopolist in the advertisers’ market;
this can be shown as an equilibrium outcome in a model in which the advertising market is
explicitly described and advertisers are allowed to multi-home (see. Gabszewicz, Laussel and
Sonnac (2002)).
33 Equilibrium prices
From the ﬁrst order necessary and suﬃcient conditions, it is straightforward to
derive the second-stage Nash equilibrium prices as
p1 =
2q1(q1 − q2) − 3s q1
4q1 − q2
(1)
p2 =
q2(q1 − q2) − s(2q1 + q2)
4q1 − q2
iﬀ s ≤
q2(q1−q2)
(2q1+q2) .This condition is necessary and suﬃcient for p2 in (1) to be pos-
itive. It is suﬃcient to guarantee that p1 > 06. The corresponding equilibrium
proﬁts are given by
π1 =
￿
s + 2q1
4q1 − q2
￿2
(q1 − q2) (2)
π2 =
￿
2s + q2
4q1 − q2
￿
q2(q1 − q2)
q1
.
For s ∈
￿
q2(q1−q2)
(2q1+q2) ,q1 − q2
￿
, we obtain
p1 =
q1 − q2 − s
2
(3)
p2 = 0,
with corresponding equilibrium proﬁts
π1 =
(s + q1 − q2)
2
4(q1 − q2)
(4)
π2 =
s(q1 − q2 − s)
2(q1 − q2)
and, ﬁnally, p1 = p2 = 0 when s ≥ q1 − q2 with proﬁts π1 = s and π2 = 0.
It is interesting to notice that, for given qualities q1 and q2, the equilibrium
prices of the two newspapers are decreasing in the advertising revenue per reader
s. However there is not a full pass-through of advertising revenues into lower
newspapers prices. Indeed the total receipts per reader pi + s, i = 1,2, are
increasing in s whereas they should be constant in the case of a full pass-through.
6Indeed q1 > q2 =⇒ s ≤
q2(q1−q2)
(2q1+q2) < 1
3(q1 − q2) =⇒ p1 > 0.
44 Equilibrium qualities
Diﬀerentiating π1 with respect to q1 we obtain when q2 ≤ 2s
∂π1
∂q1
= 0 for q1 ≤ q2 + s (5)
∂π1
∂q1
=
(q1 − q2)2 − s2
4(q1 − q2)2 ≥ 07 when q2 + s ≤ q1.
It is worthwhile to notice that q2 ≤ 2s =⇒
q2(q1−q2)
(2q1+q2) < s for all q1 ≥ q2. When
q2 > 2s we then obtain
∂π1
∂q1
= 0 for q1 ≤ q2 + s (6)
∂π1
∂q1
=
(q1 − q2)2 − s2
4(q1 − q2)2 ≥ 0 when q2 + s ≤ q1 ≤
q2(s + q2)
q2 − 2s
∂π1
∂q1
=
(s + q1)(2q1(4q1 − 3q2 − s) + q2(7s + 4q2))
(4q1 − q2)3 > 0, when q1 ≥
q2(s + q2)
q2 − 2s
.
We conclude that the proﬁt of the high quality newspaper 1 is an overall in-
creasing function of its quality on the interval [0,1] when q2 + s < 1. It follows
that q1 = 1 is a best reply to any q2 ∈ [0,1 − s). Any q1 ∈ [0,1] is a best reply
to any q2 ≥ 1 − s.
Diﬀerentiating π2 with respect to q2 we obtain, for s ∈ [0, 10−
√
96
2 q1]
∂π2
∂q2
= 0 when q2 ≥ q1 − s (7)
∂π2
∂q2
= −
s2
2(q1 − q2)2 < 0 when q2 ∈ [0,A] ∪ [B,q1 − s]
∂π2
∂q2
= −
q1(4sq2
2(2s + q2) + q2
1(4s2 − q2
2) + q1q2(−12s2 + 8sq2 + 7q2
2))
4(q1 − q2)3q2
2
when s ∈ [A,B], (8)
where A =
q1−s−
√
q2
1+s2−10sq1
2 and B = [
q1−s+
√
q2
1+s2−10sq1
2 . Notice that
[A,B]  = ∅ iﬀ s ∈ [0, 10−
√
96
2 q1).
On the other hand, for s ∈
￿
10−
√
96
2 q1,q1
￿
, we get
∂π2
∂q2
= 0 when q2 ≥ q1 − s (9)
∂π2
∂q2
= −
s2
2(q1 − q2)2 < 0 when q2 ∈ [0,q1 − s].
50.2 0.4 0.6 0.8 1
s
0
0.1
0.2
0.3
0.4
0.5
q2
Figure 1: q2 as a function of s
Proposition 1 There exists a critical level of the revenue per reader for which
the low-quality newspaper’s editor chooses at equilibrium to provide the lowest
possible quality newspaper and sells it at a zero price. More precisely, if s ∈ ￿ 1
13,1
￿
then q∗
2 = p∗
2 = 0.
In fact, it is easy to provide a more complete description of the subgame
perfect equilibria of the two stage game described above, as a function of
the advertising revenue per reader, which is provided in the following state-
ment. (i) If s ∈ [0, 1
13], then q∗
1 = 1, q∗
2 = 3s+2+
√
4−23s2−44s
4s+7 =⇒ p∗
1 =
19s+12s2−10+2
√
4−23s2−44s
−26−13s+
√
4−23s2−44s ; (ii) if s ∈
￿ 1
13,1
￿
then q∗
2 = p∗
2 = 0, q∗
1 = 1,p∗
1 = 1−s
2 .
Proof. see Appendix.
Proposition 1 shows that when advertising income per reader increases from
0 the quality of the low quality newspaper decreases until s reaches 1
13 and then
jumps down discontinuously toward the minimum quality (see Figure 1 below)
while, simultaneously, it begins to be freely distributed to its readers.
The behavior of the price p1 of the high quality journal as the advertising
revenue per reader increases is surprisingly non-monotonic (see ﬁgure 3). As
s rises from 08 the price p1 ﬁrst decreases slowly, takes a minimum value at
s = 1
23(13
√
3−22) (≃ 0.0224635) and then rises until s reaches its critical value
of 1
13. At this point p1 jumps upward discontinuously from 7
26 toward 12
26 and
then decreases steadily as s continues to increase. This enlightens somehow the
nature of the quality choice of the low-quality newspaper’s editor who chooses,
when s reaches its critical value, to select the minimum quality level in order to
elicit a corresponding discontinuous price increase from the high quality ﬁrm.
The intuition behind the choice of quality q2 is ﬁnally a simple one. the
increase in advertising revenue per reader induces the low quality editor to relax
8p1(0) = 1
4
60.2 0.4 0.6 0.8 1
s
0
0.02
0.04
0.06
0.08
p2
Figure 2: p2 as a function of s
0.2 0.4 0.6 0.8 1
s
0.1
0.2
0.3
0.4
0.5
p1
Figure 3: p1 as a function of s
70 . 2 0 . 4 0 . 6 0 . 8 1
s
0 . 0 2
0 . 0 4
0 . 0 6
0 . 0 8
0 . 1
0 . 1 2
π 2
0 . 2 0 . 4 0 . 6 0 . 8 1
s
0 . 2
0 . 4
0 . 6
0 . 8
1
π 1
0 . 2 0 . 4 0 . 6 0 . 8 1
s
0 . 2
0 . 4
0 . 6
0 . 8
1
π 1+π 2
Figure 4: Variation of newspapers’ proﬁts with s
competition by eliciting price increases of its competitor through its own quality
decrease. Since readers are more and more valuable as s increases, gaining more
readers with a low preference for quality becomes the primary objective of the
newspaper 2’s editor.
5 Proﬁts, Consumers Surplus and Welfare
Newspapers’ proﬁts are globally increasing with s, indicating that the addi-
tional beneﬁts derived from the advertising market are not (fully) passed on to
the readers. Moreover the introduction of minimum quality- free newspapers
induces an upward jump in ﬁrms’ proﬁts which is due to the sudden increase in
the price of the high quality journal. Notice that it is the traditional newspaper
sold at a positive price which most beneﬁts from higher advertising receipts per
reader: its proﬁts monotonically increase with s with an upward jump at the
critical value. Proﬁts of free newspapers ﬁrst increase and then decrease with s
(see ﬁgure 4).
The variation of consumers surplus when advertising revenue per reader in-
creases is depicted in Figure 5. It is globally decreasing with s with a downward
jump at the point where the low quality newspaper becomes a free (minimum
quality) one. This is easily explained by the decrease in the quality of newspa-
per 2 together with the jump of the price of newspaper 1 at the discontinuity
point..
It is obvious from a simple comparison of Figures 4 and 5 above that the
money which is poured by the increase in the advertising revenue per reader
does not globally beneﬁt to the readers but rather to the newspapers’ editors
and speciﬁcally to the high quality one.
6 Conclusion
80.2 0.4 0.6 0.8 1
s
0.05
0.1
0.15
0.2
0.25
0.3
SC
Figure 5: Variation of readers’ surplus with s
In this paper we have obtained an endogenous explanation for the existence
of free newspapers cohabiting with traditional ones as resulting from growing
advertising revenues per reader. Beyond a given threshold value, this increase
leads to a discontinuous decrease in the price and quality of the low quality
newspaper and simultaneously to an increase of the price of the high quality
one. Furthermore, this is unambiguously detrimental to the readers. As usual,
these conclusions should be taken with the usual caveat imposed by a theoretical
capture of real life phenomena : only a restricted domain of these are taken into
account by our model. Nonetheless, our approach provides a signiﬁcant insight
to explain the recent growth of the free daily press, which seems to upset the
media landscape in several countries.
Appendix
Proof of Proposition 1:
Whenever s ∈ (0,1) there always exist neighborhoods of 0 and q1 − s re-
spectively where π2 is strictly decreasing in q2 (see (7) and (9). above). When
s ∈
￿
10−
√
96
2 q1,q1
￿
we know that π2 is strictly decreasing in q2 on the whole
open interval (0,q1 − s) and then equal to 0, so that it takes its maximum value
at q2 = 0.When s ∈ [0, 10−
√
96
2 q1] it is easy to check that, when s ≤ 1
23q1, π2
(as deﬁned in (2) ) takes its maximum value on [A,B] at an interior point of
this non-empty interval, namely qI
2 =
3sq1+2q2
1+
√
4q4
1−23s2q2
1−44sq3
1
4s+7q1 .
Though π2 is discontinuous at A and B there are clearly in this case only
two candidate best replies to any q1 > s which are q2 = 0 and q2 = qI
2. Since
these two values are < 1 − s the unique best reply by ﬁrm 1 to either of them
is q1 = 1. Replacing q1 by 1 and comparing ﬁrm 2’s proﬁts at q2 = 0 and
90.2 0.4 0.6 0.8
q2
0.01
0.02
0.03
0.04
0.05
π2
Figure 6: π2 as a function of q2 (s = 0.05)
0.2 0.4 0.6 0.8 1
q2
0.01
0.02
0.03
0.04
π2
Figure 7: π2 as a function of q2 (s = 0.1)
q2 = qI
2 it is straightforward to see that π2(qI
2,s) > (resp. <) π2(0,s) if s <
(resp. >) 1
13.Of course π2(qI
2, 1
13) = π2(0, 1
13). Finally it is easy to check that
1
13 < 10−
√
96
2 and 1
13 < 2
23.
When . s > 2
23q1 (but s < 10−
√
96
2 q1 so that [A,B] is non empty) we see from
(2) that π2 is a decreasing function of q2 on [A,B]. The only two candidate best
replies to any q1 > s are now q2 = 0 and q2 = A. One can check that q2 = 0
always yields a higher proﬁt to ﬁrm 2. Since this value is strictly smaller than
1 − s the unique best reply by ﬁrm 1 is q1 = 1. Figure 7 illustrates this case.
￿
10References
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media market, Journal of Economics and Management Strategy 12, 291-
325
[3] Gabszewicz J.J., Laussel D. and N. Sonnac (2001), Press advertising and
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political diﬀerentiation of newspapers, Journal of Public Economic Theory
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forthcoming in Economics Letters
11Département des Sciences Économiques
de l'Université catholique de Louvain
Institut de Recherches Économiques et Sociales
Place Montesquieu, 3
1348 Louvain-la-Neuve, Belgique
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