We consider a model of daily newspapers’ competition to test the validiity of the so called “theory of the circulation spiral”. According to it, the interaction between the newspapers and the advertising markets drives the newspaper with the smaller readership into a vicious circle, finally leading it to death. In a model with two newspapers, we show that, contrary to this conjecture, the dynamics envisaged by the proposes of the theory, does not always lead to the elimination of one of them.

Jean, GABSZEWICZ

N., SONNAC

P.G., GARELLA

English

Research Papers in Economics

Département des Sciences Économiques
de l'Université catholique de Louvain
Newspapers’ market shares 
and the theory of the circulation spiral
J. J. Gabszewicz, P.P. Garella and N. Sonnac
Discussion  Paper   2005-59CORE DISCUSSION PAPER
2005/84
Newspapers’ market shares and the theory of the
circulation spiral
J.J. Gabszewicz1, P.G. Garella2 and N. Sonnac3
November 14, 2005
Abstract
We consider a model of daily newspapers’ competition to test the valid-
ity of the so called “theory of the circulation spiral”. According to it, the
interaction between the newspapers and the advertising markets drives the
newspaper with the smaller readership into a vicious circle, ﬁnally leading it
to death. In a modelwith two newspapers, we show that, contrary to this
conjecture, the dynamics envisaged by the proposers of the theory, does not
always lead to the elimination of one of them.
1CORE, Universit´ e Catholique de Louvain
2Department of Economics, University of Bologna
3CREST-LEI and Universit´ e Paris II1 Introduction
The daily newspaper industry has been the object of several empirical stud-
ies documenting a dramatic tendency to concentration (see, for instance,
Bagdikian (1980), Dertouzos, J.N and W.B. Trautman (1990), Gesenove
(2003), Kaitatzi-Witlock, S.(1996), or Rosse (1980)). One possible expla-
nation of this phenomenon is called the theory of the circulation spiral, orig-
inally proposed by the media scholar Furhoﬀ (1973). The main point of this
theory is well synthesized by the following quotation:
”the larger of two competing newspapers is favoured by a process
of mutualreinforcement between circul ation and advertising, as
a larger circulation attracts advertisements, which in turn at-
tracts more advertising and again more readers. In contrast, the
smaller of two competing newspapers is caught in a vicious cir-
cle; its circulation has less appeal for the advertisers, and it loses
readers if the newspaper does not contain attractive advertising.
A decreasing circulation again aggravates the problems of selling
advertising space, so that ﬁnally the smaller newspaper will have
to close down” (Gustafsson (1978), p. 1)1.
In this note we provide a simple duopoly model of the daily press mar-
ket in order to test whether the dynamics implicit into the circulation spiral
leads indeed to the elimination of one of the competitors, as predicted by the
theory. The circulation spiral argument for elimination rests crucially on the
implicit assumption that readers are not only interested in reading the news,
but also into canvassing advertisements in newspapers, in particular classiﬁed
ads. While the reader’s taste for one or the other newspaper clearly depends
upon the way news are represented, e.g. by the political view patronized
by the newspaper, the utility of reading an ad is rather independent of the
political color of the newspaper reporting it. Notice further that a reader can
always ignore the ads if he wants to do so. Thus, contrary to what happens
1Several other elements have been proposed to explain this tendency to concentration
in the daily press industry, like the existence of large economies of scale (Rosse 1967)or
the two-sided market structure of the press and advertising industries (Gabszewicz et al.
2004).
1for medias like television and radio, ads may not diminish the utility of read-
ing, somewhat supporting the assumption of this theory. The combination
of pol iticaland commercialinformation makes of a newspaper a good with
two main characteristics. Buyers are interested in consuming these charac-
teristics rather than the good itself. Thus, it is natural to represent a typical
reader as endowed with some political opinion, ”leftist” or ”rightist”, say,
and with a desire to learn about buying and selling opportunities through
reading commercials. The importance attached to the political color of the
newspaper, however, varies across readers of both camps. To some extent a
reader should be willing to accept to read a newspaper of a diﬀerent political
orientation, provided he gets enough beneﬁt from the amount of commer-
cials to be canvassed in it. Our model tries to reﬂect the above elements in
the simplest possible way, keeping its ingredients as close as possible to the
informal set-up of the theory initially proposed by Furhoﬀ.
We ﬁnd that the concl usions drawn from this informalproposalmust
be qualiﬁed. It is not always true that the circulation spiral leads to the
elimination of one of the competitors. Several elements play a role in driving
the dynamics of the competitors’ market shares, like the intensity of readers’
preferences for ads, or the number of leftists in the readership, compared with
the one of rightists. We ﬁnd a necessary and suﬃcient condition on these
magnitudes that governs whether the minority newspaper is able to survive
when the circulation spiral evolves, granting that elimination never occurs
and that the market shares stabilize at a long-run equilibrium level.
2 The model
Consider a population of readers split into two types; the ﬁrst (respectively
second) type consists of all leftist (respectively, rightist) readers and is uni-
formly distributed on the interval [0,1] with mass of readers λ1 (respectively,
λ2 =1− λ1 ): at each point m in [0,1],there corresponds a number λi, with
i =1 ,2, of similar readers. Accordingly, the total mass of the readership is
equalto λ1 + λ2 = 1. Readers choose their newspaper in accordance with
their political preferences and the amount of commercials included in it. We
denote by ai the amount of commercials included in a copy of newspaper
i. For readers of type 1, represented by the point m in [0,1],the utility for
2reading newspaper 1 is equalto
u1(1,m)=m + sa1, (1)
while their utility for reading newspaper 2 is equal to
u1(2,m)=sa2, (2)
and similarly for the readers of type 2 represented by the same point m,
with the appropriate change of indices. The parameter s, identicalfor al l
readers, measures the intensity of readers’ attraction for advertising. The
totalnumber of advertisers is equalto A, A<1, and each of them has a
one unit advertising budget to be allocated between the two newspapers. We
assume that each of them allocates this unit in proportion to the size of their
readership2. Therefore we get
ai = λiA, for i =1 ,2. (3)
Readers represented by point m and belonging to type 2 buy newspaper 2 if,
and only if,
u2(2,m)=m + sa2 ≥ sa1 = u2(1,m),
or else,
m ≥ s(a1 − a2). (4)
Accordingly, when the number of commercials in the leftist newspaper
exceeds that in the rightist one, the fraction of rightist readers who switch to
newspaper 1 has measure s(a1−a2), while their mass is equal to λ2s(a1−a2).
Obviously, when a2 >a 1 , this measure is equalto zero and the switch occurs
from left to right.
3 Dynamics
Now we analyze how the readership sizes evolve over time as a consequence of
an initial asymmetry in their relative sizes. Without loss of generality,assume
2This behavior corresponds, for instance, to the choice by an advertiser maximizing the
utility of money spent in advertising, when the utility function is given by a
λ1
1 a
λ2
2 subject
to the budget constraint a1+a2 = 1. In that case the solution implies that the ratio a1/a2
is equal to λ1/λ2. Therefore the total advertising amount in paper i is equal to λiA.
3that initially the leftist readership exceeds the rightist one, namely, λ1 >λ 2.
We shall denote by n1(t) and n2(t) the readership sizes at time t, so that
λ1 and λ2 are the readership sizes n1(0) and n2(0) of the two newspapers at
time 0.
We suppose that advertisers know these sizes at date 0 and send, before
the ﬁrst issues are printed, their commercials to the two newspapers, accord-
ing to the corresponding proportions, namely, ai(0) = λiA. This implies that
a1(0) >a 2(0). Due to the insertion of these commercials into the newspapers,
the utility from buying newspaper 1 is increased for both types of readers
and some readers decide to switch at date 1 from the rightist to the leftist
one, which determines a ﬁrst change in the readership sizes, namely
n1(1) = λ1 + sλ2 [a1(0) − a2(0)]
n2(1) = λ2 − sλ2 [a1(0) − a2(0)].
Clearly, n1(1) is larger than n1(0), while the readership of newspaper 2 gets
smaller of the same amount (namely sλ2 [a1(0) − a2(0)]).
At date 1, advertisers react, before a new issue goes to print, to these
new readership sizes so that we get a1(1) = n1(1)A. This engenders again a
new switch from rightist readers to the leftist newspaper, at date 2, which
determines new readership sizes at time 2 given by the equation
n1(2) = λ1 + sλ2 [a1(1) − a2(1)]
= λ1 + sλ2A[n1(1) − n2(1)]
and, obviously, n2( 2 )=1− n1(1).
More generally, we have
a1(t)=n1(t)A,
so that
n1(t +1 )=λ1 + sλ2A[n1(t) − n2(t)].
Since n2(t)=1− n1(t), we get
n1(t +1 )=λ1 + sλ2A[2n1(t) − 1].
This ﬁrst-order linear diﬀerence equation has, as unique solution, the expres-
sion
n1(t)=
sλ2A(2λ1 − 1)
2sλ2A − 1
(2sλ2A)
t +
λ1 − sλ2A
1 − 2sλ2A
. (5)
4When β =2 sλ2A>1 holds, the coeﬃcient of the term (2sλ2A)
t in
(5) is strictly positive (recalling that it has been supposed that λ1 >λ 2).
Moreover, β>1 implies that the expression β
t tends to +∞ when t tends
to +∞. Consequently, the trajectory corresponding to the above diﬀerence
equation diverges to +∞ when t goes to +∞: the leftist newspaper attracts
more and more readers over time, and at an increasing speed, due to the
increase in the number of commercials; at some date, the rightist newspaper
readership collapses to zero and the newspaper is eliminated. Now, suppose
that β<1 holds instead. Then we have 2sλ2A<1 and the coeﬃcient of
the term (2sλ2A)
t is now negative. Moreover, since β is smaller than one,
the expression β
t is decreasing with t and tends to 0 when t goes to +∞,s o
that the sequence corresponding to the ﬁrst term in the diﬀerence equation
approaches 0 by negative values when t tends to +∞.3 Finally, the whole
expression is increasing with t and converges to the constant n∗
1, namely
lim
t→∞n1(t)=n
∗
1 ≡
λ1 − sλ2A
1 − 2sλ2A
and lim
t→∞n2(t)=n
∗
2 =1−
λ1 − sλ2A
1 − 2sλ2A
. (6)
where we notice that n∗
2 is always positive, however small is λ2 > 0, so
that there is no minimalinitialreadership needed to obtain survival . We
may summarize the above discussion in the following way. Either β>1
and the rightist newspaper is necessarily eliminated after some period of
time, or β<1 and the market share of the leftist newspaper necessarily
converges to the value n∗
1. Then a naturalquestion arises: can this l imit n∗
1
be larger than the total readership size? If the answer is yes, it means that
the leftist newspaper becomes a monopolist after some period of time, as
conjectured by the theory of the circulation spiral. If, on the contrary, this
limit is smaller than the total readership size, then some room is left for the
minority newspaper to survive for ever. The next proposition answers this
question without any ambiguity.
Proposition 1 Both newspapers keep strictly positive market shares over all
periods if and only if the ”survival condition”
2sλ2A<1
is satisﬁed.
3It is easy to check that all terms in the sequence {n1(t)} are strictly positive because
the sequence itself is increasing, so that n1(t) >n 1(0).
5Proof : The necessary part of the proposition has already been proved
above: the survivalcondition has to be satisﬁed for otherwise the trajectory
of n1(t) diverges and leads to the elimination of the rightist newspaper. Now
let us show that this condition is also suﬃcient. Suppose on the contrary that
the survival condition holds and that the rightist newspaper is eliminated.
Under the survivalcondition,we know that the whol e expression in (5) is
increasing with t and converges to the constant n∗
1 in (6) when t →∞ . Since
we have assumed that the rightist newspaper is eliminated at the limit, we
must have n∗
1 > 1. It is easy to check that this inequality contradicts the
survivalcondition β<1. Q.E.D.
Notice that, for avoiding the elimination of newspaper 2, the larger is the
ad-attraction intensity s, the lower must be the number of advertisers, A,
all other things being equal. Further, since newspaper 2 is the minority one,
we know that 2λ2 < 1, and therefore the inequality s<1/A is a suﬃcient
condition for survival.
Figure 1 depicts the trajectory of n1(t) in both cases, β>1 and β<1.
The elimination date, denoted by t∗, is also depicted in ﬁgure 1. The exact
expression for t∗ can be recovered by setting n1(t) = 1 in (5) above (letting
R =( sA − 1)/(sA(2λ2 − 1)) one has t∗ =ln β/lnR). It can be seen, that
t∗ is increasing in λ2, which indicates that the larger the minority, the longer
the life period for the minority newspaper, even if, ﬁnally, elimination is to
be the end of the process.4
4 Conclusion
We have outlined a bare-bones model of the circulation spiral where, ac-
cording to the corresponding theory, only the crude forces put in motion
by pure demand-side eﬀects are analyzed. Our main conclusion is that the
elimination of daily newspapers cannot be explained only by these eﬀects
when the survivalcondition is satisﬁed. This hinges upon the importance of
advertising in the utility function of the readers, and upon the size of the
minority readership, lower minorities being better apt to survive, all other
4To be precise, the partial derivative of t∗ with respect to λ2 is found to be equal to  
ln(R) 1
λ2 +
 
2(As−1)ln(2sλ2A)
As(1−2λ2)2
  
(ln(R))
−2.
61
n* 1
n1(0)
n1(t)
β<1
β>1
t t*
Figure 1:
things equal. However, when the survival condition is violated, the larger
the minority the longer the life of the newspaper representing it. In conclu-
sion, other elements should necessarily be taken into account to ground the
circulation spiral theory on ﬁrmer roots, and improve the understanding of
the concentration phenomena in the daily newspaper markets.
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8Département des Sciences Économiques
de l'Université catholique de Louvain
Institut de Recherches Économiques et Sociales
Place Montesquieu, 3
1348 Louvain-la-Neuve, Belgique
 ISSN 1379-244X         D/2005/3082/059

Conglomerate, concentration, and the media.

Daily newspapers, monopolistic competition and economies of scale.

Economic eﬀects of media concentration: estimates from a modelof the newspaper ﬁrm.

Pluralism and media concentration in Europe.

Press Concentration and Monopoly: New Perspectives on Newspaper ownership and Operation:.

Some reﬂections on newspaper concentration. The Scandinavian Economic History Review,

Sonnac (2004). Attitudes toward advertising and price competition in the press industry.

Newspapers’ market shares and the theory of the circulation spiral

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