Calling s Recei ing Pa y Pays: Ma ke Pene a ion and he
Impo ance o he Call Ex e nali y∗
Tommaso Maje †
Uni e si a Au `onoma de Ba celona
Tommaso.Ma[email p o ec ed]
Michele Pis olla o‡
Uni e si a Au `onoma de Ba celona
Michele.Pis olla [email protected]
Oc obe 21, 2010
Abs ac
In his pape we s udy how he access p ice a ec s he choice o he a i egime
aken by he ne wo k ope a o s. We show ha o high alues o he access p ice, ha
is aken as a pa ame e by he i ms, ne wo ks decide o cha ge only he calle s. O he -
wise, o low alues o he access cha ge, ne wo ks cha ge also he ecei e s. Mo eo e ,
we compa e ma ke pene a ion and o al wel a e be ween he wo p ice egimes. Ou
model sugges s ha , o high alues o call ex e nali y, ma ke pene a ion and o al
wel a e a e la ge in Recei ing Pa y Pays egime when he access cha ge is close o
ze o.
JEL Classi ica ion:L96, L50
Keywo ds: Telecommunica ions, Mobile e mina ion a es, Calling Pa y Pays egime,
Recei ing Pa y Pays egime, Incomple e Co e age, Call Ex e nali y, Ma ke Expansion,
Regula ion
∗We a e g a e ul o Sjaak Hu kens, Xa ie Ma `ınez Gi al , Da id P´e ez Cas illo and F ancesc T illas.
†Depa amen d’Economia i d’His `o ia Econ`omica, Edi ici B, 08193 Bella e a (Ba celona), Spain.
‡Depa amen d’Economia i d’His `o ia Econ`omica, Edi ici B, 08193 Bella e a (Ba celona), Spain.
1
1 In oduc ion
In o de o p o ide in e connec ion among all use s, elecom ne wo ks need access o i al’s
consume s. Access is p o ided a e he paymen o a e mina ion cha ge (o access p ice).
This cha ge is a pa o he cos o o -ne calls and consequen ly a ec s he p ice o calls.
Las yea s in Eu ope ha e seen a g owing discussion among egula o y au ho i ies
abou egula ion o e mina ion cha ges o access p ices. On he one hand, he Eu o-
pean Commission (2008, 2009) ecommended o lowe e mina ion cha ges in o de o
lowe a e age p ice pe minu e. On he o he hand, some o hem (e.g. O com, he
UK elecommunica ions egula o ) a e wo ied ha his could b ing ne wo k ope a o s o
cha ge consume s o ecei ing a call o , in o he wo ds, o swi ch om a Calling Pa y
Pays (CPP) egime, whe e only calle s pay o making a call, o a Recei ing Pa y Pays
(RPP) egime, whe e bo h calle and ecei e pay o join a call.
O com has exp essed se e al conce ns abou he in oduc ion o a RPP a i egime.1
The main objec ions o he UK elecommunica ions egula o y au ho i y a e ha i would
be dis up i e o cus ome s, i would mee wi h consume esis ance and i migh also lead
o cus ome s u ning o hei mobile phones. The e exis many wo ks abou his las
conce n (e.g. Bomsel e al. (2003), Cadman (2007) and Sama aji a & Melody (2000)) bu
hey a e no p o iding a heo e ical backg ound o hei analysis. In pa icula , he e is
no any model which explain how ma ke pene a ion and wel a e would change swi ching
om one egime o he o he . Ou in en ion is o model he wo a i egimes and p o ide
a heo e ical amewo k o compa e hem.
Li lechild (2006) epo s some di e ences be ween he wo egimes. Some da a a e
summa ized in Table 1.
In RPP coun ies minu es o usage a e mo e han in CPP coun ies. To unde s and
he eason o ha , i is impo an o no ice ha RPP coun ies usually adop Bill & Keep
(BaK) as in e connec ion a angemen . This means ha ne wo k ope a o s pay a p ice
equal o ze o (o close o) in o de o e mina e phone calls. Hence, a BaK policy educes
he ma ginal cos s o a ic and he e o e usage p ices, leading o highe usage.
In 2005 ma ke pene a ion in US and Canada is a below pene a ion in EU bu
in o he BaK coun ies as Hong Kong pene a ion is abo e EU a e age. O he da a o
2008 in ERG (2009)2show ha US pene a ion o 87% is lowe han EU a e age o 123%.
Howe e , pene a ion in Hong Kong and Singapo e is abo e EU a e age. F om hese da a
seems ha ma ke pene a ion is lowe in BaK coun ies, bu in CPP coun ies pene a ion
1See O el (2002) and O com (2005).
2See ERG (2009), Nex Gene a ion Ne wo ks Fu u e Cha ging Mechanisms / Long Te m Te mina ion
Issues.
2
Min. o use (pe mon hs) Pene a ion (%, 2005)
RPP coun ies
USA 630 61
Canada 359 47
Hong Kong 387 106
Singapo e 282 90
CPP coun ies
UK 151 104
Ge many 76 87
F ance 225 74
I aly 120 110
Spain 135 99
Table 1: Mobile ma ke s uc u e in selec ed coun ies (2005).
migh be o e s a ed because o he adi ionally g ea e numbe o p epaid schemes and
mul iple SIM ca ds.3
In his pape we p o ide a heo e ical analysis o show how he choice o he access
p ice de e mines he e ail p icing egime: ou model con i ms ha CPP is a choice o he
elecommunica ions indus y in esponse o access p ices abo e e mina ion cos . O he -
wise, o access p ices below cos , ne wo ks p e e o cha ge ecei e s as well. Mo eo e ,
we compa e ou p edic ions o wo egimes wi h ac ual da a in o de o gi e some indica-
ions o he egula o . I u ns ou ha wi h high call ex e nali y, a BaK policy (which is
associa ed o RPP egimes) implies highe usage and highe ma ke pene a ion. This is
because highe usage inc eases u ili y o joining a mobile ne wo k and consequen ly mo e
people would like o join a ne wo k. Mo eo e , BaK maximizes social wel a e wi h espec
o any o he policy.
Ou model s esses he ele ance o he call ex e nali y ( he u ili y ha consume s
3A epo o Analysis Mason (2008, pag. 8) o O com says:
While looking a he compa a i e s a ics, i is impo an o no e ha he s anda d pene a ion
da a [. . . ] measu es he numbe o subsc ip ions in ci cula ion, and no he numbe o use s
who hold mobile subsc ip ions, which in he case o Hong Kong, Singapo e and he UK is
much lowe [. . . ].
3
ob ain o ecei ing a call). Indeed, as he Eu opean Commission (2008) ema ks, he
wel a e-maximize policy abou he access p ice may be e y di e en o di e en alues
o he call ex e nali y. Fo low alues ou model sugges s ha he op imal policy is o se
he access p ice close o he e mina ion cos and, consequen ly, o induce he indus y o
adop a CPP p ice egime. O he wise, o high alues o call ex e nali y, he op imal policy
should be BaK (in his case he indus y would adop a RPP egime). The eason is ha
RPP egimes in e nalize he call ex e nali y by making he ecei e paying o ecei ing
he call.4Hence, when his ex e nali y is ele an , RPP egimes a e mo e e icien .
Rela ed li e a u e. The main con ibu ion o he li e a u e on elecommunica ions is
gi en by he seminal pape s by A ms ong (1998) and La on e al. (1998a,b). In hei
pape s hey model elecommunica ions compe i ion be ween wo ne wo k ope a o s ha
compe e o consume s ha ob ain u ili y only om making calls. La on e al. (1998a)
analyze ne wo k in e connec ion in an un egula ed en i onmen whe e p ice disc imina-
ion is excluded. They show ha o non-linea e ail p ices, high in e connec ion a i s
aise inal e ail p ices and educe social wel a e. Gans & King (2001) co ec ed he abo e
analyses and ound ha , unde p ice disc imina ion and non-linea p icing, ne wo ks p e-
e an access p ice below cos .5
These pape s inspi ed many wo ks. Jeon e al. (2004) ex end hese models and allow
consume s o ob ain u ili y om ecei ing calls. In he usual se up o wo ho izon aly
di e en ia ed ne wo ks wi h ull co e age o he ma ke , hey in oduce he possibili y o
ope a o s o cha ge cus ome s also o ecei ing a call. Hence ecei e s may a ec olume
o he calls by hanging up i s . The au ho s de i e equilib ium usage p ices unde di e en
o -ne p icing a i s. On he one hand, wi hou ne wo k based disc imina ion, ne wo ks
se p ices equal o he pe cei ed ma ginal cos . On he o he hand, in p esence o ne wo k
based disc imina ion, ne wo ks se high o -ne p ices ( o high alues o he ex e nali y,
in e connec ion b eaks down) and on-ne p ices lowe han he ma ginal cos . To a oid
mul iplici y o equilib ia, hey in oduce a noise e m in he u ili y o he ecei e .6
Cambini & Valle i (2008) use a model whe e he demand o phone calls be ween each
pai o cus ome s is join ly de e mined. They show ha unde ce ain condi ions he
connec i i y b eakdown is elimina ed. Mo eo e , hey explain he ela ionship be ween
4Fo a discussion o his opic, see BEREC (2010b).
5Fo a good su ey o he li e a u e, see A ms ong (2002).
6No ice ha he hypo hesis o ull co e age p e en s he possibili y o analyzing he e ec s o di e en
access p ice policy on he ma ke size and hei consequences on he wel a e. Indeed, in a pa ag aph he
au ho s s udy incomple e co e age bu hey limi hei analysis o he de ini ion o he equilib ium usage
p ices.
4
he access cha ge and he s uc u e o he e ail p ices chosen by he ne wo k ope a o s
(ne wo ks choose o cha ge he ecei e only i he access cha ge is su icien ly low). Lopez
(2008) ex ends Jeon e al. (2004) in ano he di ec ion. He in oduces a andom a iable
also in he u ili y o he calle . In his amewo k, ne wo ks se p ices equal o he pe -
cei ed ma ginal cos . Mo eo e , he shows ha i m’s p o i s do no depend on he access
cha ge.
Finally, He malin & Ka z (2009) allow consume s o ob ain u ili y om ecei ing calls bu ,
di e en ly om he p e ious pape s, hey assume ha ne wo ks compe e on quan i ies. I
u ns ou ha a egula o can no induce e icien o -ne p ices h ough he access cha ge.
In his pape we modi y he amewo k desc ibed in Jeon e al. (2004) and we inco po a e
ma ke expansion in he benchma k model o compa e equilib ium p ices (including he
ixed pa ), ma ke pene a ion and p o i s in he wo di e en a i egimes. Unde no
ne wo k-based disc imina ion, we conside he case whe e ne wo ks cha ge a s ic ly posi-
i e cha ge o he ecei e s (Recei e Pa y Pays egime) and he case whe e ne wo ks do
no cha ge consume s o ecei ing a call (Calle Pa y Pays egime).
In Sec ion 2 we p esen he model. In Sec ion 3 we cha ac e ize he equilib ium p ices
and quan i ies in he wo a i egimes. In Sec ion 4 we simula e he equilib ium esul s
and we compa e he solu ions in he wo cases. Sec ion 5 concludes.
2 The Model
We gene alize he model in oduced by Jeon e al. (2004) allowing o ma ke expansion.
Ne wo ks. We conside wo mobile ne wo ks i= 1,2 loca ed a wo poin s o an in ini e
Ho elling line. We no malize o one he dis ance be ween he wo ne wo ks. Mobile
ne wo ks incu a ixed cos pe consume and ha e on-ne call cos o c= 2c0+c1, whe e
c0is he ma ginal cos o o igina ing o e mina ing a call and c1is he ma ginal cos o
ansmi ing a call. Le adeno e he access cha ge o e mina ion cha ge. The ma ginal
cos o an o -ne call is he e o e c+ (a−c0) o he calle ’s ne wo k and c0−a o he
ecei e ’s ne wo k.
Ta i s. Mobile ne wo k io e s a mul i-pa a i (pi, i, Fi) whe e piis he calle ’s usage
p ice (no ice ha we only conside he case o non ne wo k-based disc imina ion), iis
he ecei e ’s usage p ice and Fiis he ixed pa .
5

Consume s. Consume s a e di e en ia ed along he Ho elling line. This line ep esen s
he p e e ences o he consume s o e one cha ac e is ic o he ne wo ks. Fo ins ance,
consume s may p e e he well know phone ope a o ins ead o a new one.
A consume loca ed a xand selec ing ne wo k iincu s a anspo a ion cos equal o
|x−xi|.
The u ili y o placing a call is u(q), whe e qdeno es he leng h o he call. As in Jeon
e al. (2004), we assume ha he ma ginal u ili y ha a ecei e de i es om ecei ing a
call is subjec o a noise εwhich in oduces unce ain y abou he willingness o pay o
ecei ing a call independen ly on he p ice she is paying.7Fo ins ance, i could be he
case ha he ecei e is unwilling o alk on he phone when she is d i ing o wo king
and by conside ing he noise we ha e a mo e ealis ic model. Hence he ecei e ’s u ili y
is ˜u(q) + εq and we assume ha ε ollows he dis ibu ion unc ion Fwi h suppo [¯
ε, ¯ε],
ze o mean and densi y . Fo simplici y we conside ˜u(q) = βu(q), wi h β > 0. The len gh
o calls is de e mined by he i s one who in e up s he con e sa ion. The calle equa es
he ma ginal u ili y o he usage p ice piand she would hang up when he ma ginal u ili y
is pi.
The ecei e equa es he ma ginal u ili y ˜u′+ε o he ecei ing p ice i. The e o e he
ecei e will sol e βu′+ε= j o u′and he e o e he would hang up when u′is j−ε
β.
Hence, he olume o calls is q(max{pi,( j−ε)/β}).
The olume o calls is de e mined by he pai (pi, j) and a ealized alue εo he
andom a iable:
D(pi, j) =h1−F( j−βpi)iq(pi) + Z j−βpi
¯
ε
q j−ε
β (ε)dε. (1)
This means ha wi h p obabili y [1 −F( j−βpi)] he calle hangs up i s and he call
las s q(pi) minu es. Wi h p obabili y F( j−βpi) he ecei e hangs up i s and he call
las s q( j−ε
β) minu es. The e o e ne wo k idoes no know a p io i who will be he i s
one o hang up and consequen ly, who will de e mine he leng h o he call.
Conside a consume in ne wo k i. He u ili y o calling a consume in ne wo k jis:
U(pi, j) =h1−F( j−βpi)iu(q(pi)) + Z j−βpi
¯
ε
uq j−ε
β (ε)dε. (2)
He u ili y om ecei ing calls om a consume ha joined ne wo k jis:
˜
U(pi, j) = Z¯ε
j−βpih˜u(q(pi)) + q(pi)εi (ε)dε+
+Z j−βpi
¯
εh˜uq j−ε
β+q j−ε
βεi (ε)dε+ (3)
7This noise esul s in a posi i e p obabili y o bo h he calle and he ecei e o hanging up i s .
6
The e o e, we can w i e he ne su plus o a consume ha joined ne wo k ias ollows:
wi= 0+niU(pi, i) + njU(pi, j) + ni˜
U(pi, i) + nj˜
U(pj, i)
−pihniD(pi, i) + njD(pi, j)i− ihniD(pi, i) + njD(pj, i)i−Fi(4)
whe e 0is a subsc ibe ’s u ili y om o he mobile se ices.
The p o i s o ne wo k ia e gi en by:
πi=nihni(pi−c)D(pi, i) + nj[pi−c−(a−c0)]D(pi, j) + nj(a−c0)D(pj, i)
+ iniD(pi, i) + njD(pj, i)+Fi− i(5)
whe e ni(pi−c)D(pi, i) a e he p o i s pe use o making on-ne calls, nj[pi−c−(a−
c0)]D(pi, j) a e he p o i s pe use o making o -ne calls, nj(a−c0)D(pj, i) a e he
p o i s o e mina ing o -ne calls, i[niD(pi, i)+njD(pj, i)] a e he p o i s o ecei ing
calls, Fiis he ixed pa o he mul i pa a i and is he cos pe cos ume .
No ice ha he exp ession o he p o i s akes di e en o ms when he calle o he
ecei e de e mines he leng h o he call. On he one hand, when βpi< j he ecei e
will hang up i s and hen he leng h o he call depends only on he p ice . On he o he
hand, when βpi> j he calle will hang up i s and he leng h o he call depends only
on he p ice p. Bu he ne wo k does no know who will be he i s one o hang up. To
model ha , Jeon e al. (2004) in oduce a noise elemen in he olume o calls. The e o e,
we can maximize he exp ession o he p o i s ha depends on he noise. In his case he
p o i s a e di e en iable o all posi i e p ices (pi, i).
3 The equilib ium
In o de o analyze ma ke pene a ion we conside elas ic subsc ibe pa icipa ion. Ex-
plici ly, we model consume demand as he Ho elling model wi h hin e lands.8I he wo
ne wo ks o e u ili ies w1and w2, hen ne wo k ia ac s:
ni=1
2+wi−wj
2 +λwi(6)
whe e λ≥0 ep esen s he magni ude o ma ke expansion possibili ies. This is one o
he no el ies we in oduce in ou model wi h espec o Jeon e al. (2004) because i
allows us o analyze how di e en alues o he access p ice a ec he equilib ium ma ke
pene a ion and he e ec s o he la e on wel a e. In o de o ha e non explosi e ma ke
8Fo mo e de ails see A ms ong & W igh (2009).
7
sha e λmus be small enough.9We impose:
λ < min 1
2(U pp +˜
U pp −cD pp),1
2(Ucpp +˜
Ucpp −pcppDcpp).(7)
The equilib ium is gi en by he ec o o p ices (pi, i, Fi) ha maximize ope a o i’s
p o i s as de ined by equa ion (5). The only es ic ions we impose a e he non-nega i i y
o he p ices. When he ope a o is cha ging s ic ly posi i e p ices o i s use s we ha e a
RPP egime. O he wise, i he ecei ing p ice is ze o we ha e a CPP egime.10 Unde he
assump ion o a balanced calling pa e n11, we cha ac e ize he equilib ium p ices gi en
he access cha ge.
3.1 The case a < c0: he Recei ing Pa y Pays egime
Ne wo k ope a o s a e ee o cha ge cus ome s o making and ecei ing a call. The e o e,
ne wo k ise s a calle ’s usage p ice piand a ecei e ’s usage p ice i ha maximize
consume s su plus ha will be ex ac ed h ough he ixed pa Fi. Using he usual
maximiza ion p ocedu e, he equilib ium e ail p ices a e:
P oposi ion 3.1 (Equilib ium e ail p ices).The symme ic equilib ium e ail p ices
(p, , F)a e:
p pp =c+ (a−c0)
pp =c0−a
F pp = + φ
γ(a) + [3 + γ(a)]λ
whe e γ(a)≡1−2λ[U pp(a) + ˜
U pp(a)−cD pp(a)] and φ≡1 + 2λ 0−2λ .
P oo . See appendix.
No ice ha , as in he case o inelas ic demand desc ibed by Jeon e al. (2004), he
usage p ices a e equal o he pe cei ed ma ginal cos . Mo eo e , he ixed pa is highe
9F om equa ions (15) and (20) he de i a i es o he ma ke size wi h espec o he ixed pa a e
∂N pp
∂F pp
i
=−λ
γand ∂Ncpp
∂F cpp
i
=−λ
δ.
We mus ha e γ > 0 and δ > 0.
10O he cases whe e p ices o he han he ecei ing one a e ze o can no be an equilib ium.
11This assump ion says ha he pe cen age o calls o igina ed and e mina ed on a gi en ne wo k e lec s
he ma ke sha e o his ne wo k.
8
han he ixed cos pe use as long as φ > 0. Finally, he sum o he usage p ice is
cons an and equal o he ma ginal cos c. The access cha ge de e mines he dis ibu ion
o cos be ween calle and ecei e . Fu he mo e, no ice ha γ(a) is an opposi e measu e
o he su plus o joining a call in a RPP egime (U pp +˜
U pp −cD pp), wi hou aking in o
accoun he ixed ee: he bigge is γ(a), he lowe is his su plus.
I is easy o compu e he o al size o he ma ke and he p o i s in he symme ic
equilib ium:
N pp =[γ+ (1 + γ)λ ]
γ[γ+ (3 + γ)λ ]φ(8)
and
π pp
i=N
2hF− i=γ+ (1 + γ)λ
2γ[γ+ (3 + γ)λ ]2 φ2.(9)
No ice ha , in o de o ha e posi i e equilib ium quan i ies, we ha e o impose:
φ > 0⇐⇒ λ > −1
2( 0− )i 0> ,
ha is always e i ied.12
Vanishing noise. As he noise ε ends o ze o, i can be shown ha he calle and he
ecei e demand he same leng h o communica ion when:
a=c0−βc
1 + β≡aI.
I a > aI hen he calle is de e mining he leng h o he call wi h p obabili y con e ging
o one (calle so e eign y). Gi en ha he equilib ium calling p ice is inc easing in a, by
educing he access p ice he leng h o he call inc eases. O he wise, i a < aI, he ecei e
is de e mining he leng h o he call ( ecei e so e eign y). Since he equilib ium ecei ing
p ice is dec easing in a, by inc easing he access p ice he leng h o he call inc eases.
Hence, a a=aI, he call is he longes possible.
Since he access p ice ais nonnega i e, an equilib ium whe e bo h calle and ecei e
can de e mine he leng h o a call exis s only i
β⩽c0
c−c0
<1,
o he wise in equilib ium we can ha e only calle so e eign y and he longes call happens
a a= 0.
12I 0< , we would ha e an uppe bound o λ:
λ < 1
2( − 0).
9
Leng h o a call. As usual, he demand unc ion in e ms o leng h o a call, q(·), is
a dec easing unc ion o he e ail p ices (q′<0). Mo eo e we saw ha , as he noise
anishes, he leng h o he call is de e mined by he calle wi h p obabili y con e ging o
one when a > aI.
P oposi ion 4.1 (Leng h o a call.).Calls las mo e unde RPP egime when calls ex-
e nali y is high enough, i.e.:
β≥c0
c.
I β < c0/c calls las mo e unde RPP only i he access p ice is high enough, i.e.:
c0−βc < a < c0.
P oo . See Appendix.
This p oposi ion p o ides suppo o some empi ical e idences: unde RPP egimes
he leng h o calls is signi ican ly longe han unde CPP. Acco ding wi h p oposi ion 4.1
calls a e longe unde RPP i he ex e nali y he ecei e s pe cei ed is high enough.
aI
c0
0.000
0.005
0.010
0.015
0.020
a
2000
4000
6000
8000
10000
Leng h o he call
(a) β= 0.25
aI
c0
0.000
0.005
0.010
0.015
0.020
a
2000
4000
6000
8000
10000
Leng h o he call
(b) β= 0.5
aI
c0
0.000
0.005
0.010
0.015
0.020
a
2000
4000
6000
8000
10000
Leng h o he call
(c) β= 0.75
c0
0.000
0.005
0.010
0.015
0.020
a
2000
4000
6000
8000
10000
Leng h o he call
(d) β= 1
Figu e 3: Leng h o a call q. Pa ame e alues: c0= 0.01, c= 0.02, = 1500 and η= 2.
16

We ep esen ed he leng h o a call o di e en alues o βin Fig. 3. F om now on, we
use a cons an elas ici y demand unc ion q(p) = p−η(as in Hoe nig (2007)) whe e η > 1
and u(q) = η
η−1qη−1
η. The do ed line is s ill ep esen ing he h eshold be ween ecei e
so e eign y and calle so e eign y while he dashed line sepa a es RPP egime om CPP
egime.
No ice ha he longes leng h is a ained o aI, when calle and ecei e wan o hang
up a he same ime. The eason is ha in RPP he p ice o a call is sha ed be ween calle
and ecei e , aking in o accoun he posi i e ex e nali y on he ecei e and, he e o e,
he calls end o be longe . Bu his is ue only when calle and ecei e a e eage o
hang up mo e o less a he same ime. O he wise who is bea ing he highe p ice p e e s
o end he call ea lie and, gi en ha in RPP he a ia ion o he e ail p ices is s eepe ,
he leng h o he call d ops quicke han in CPP.
Fo low alues o call ex e nali y β, BaK p oduces sho e calls han alues o access
cha ge jus abo e e mina ion cos .
Fo high alues o β(Fig. 3c and 3d) access p ices close (o equal) o ze o imply
longe calls in RPP han CPP. Since o highe alues o he ex e nali y he ecei e is
eage o pay o ecei ing a call, he alue o a ha makes calle and ecei e o hang up
a he same ime shi s owa ds ze o whe e he associa ed e ail p ices a e highe o he
ecei e . This allows he egula o o se ze o access p ice and keeping calls longe han
CPP egimes. This con i ms he expec a ion o O com (2009, pag. 37):
[. . . ] in e na ional compa isons p o ide e idence ha his ela ionship be-
ween e mina ion a es, and ake-up and usage, exis s. A simple analysis o
c oss-coun y da a [. . . ] sugges s ha coun ies ha ha e, b oadly speaking,
sys ems ha adop ecip oci y o “bill and keep”-like a angemen s – US, Hong
Kong and Singapo e (and o a lesse deg ee Canada) ha e highe usage han
coun ies wi h “Calling Pa y’s Ne wo k Pays” egimes.
Fixed pa . Fig. 4 illus a es he compa ison be ween he ixed pa in he wo p ice
egimes. Fi s , no ice ha he alue o λis chosen acco ding o equa ion (7). I is
wo hwhile o no ice ha a a=aIwe ha e he highes ixed pa in RPP. The eason is
s aigh o wa d: aImaximizes consume su plus o joining a call and he e o e ne wo ks
can ex ac a highe su plus h ough he ixed pa . Indeed his is also he eason why in
hese g aphs highe ixed a i s a e associa ed o longe calls.
Fo low alues o calls ex e nali y, he ela ionship be ween equilib ium alues in RPP
and in CPP is no uni ocally de e mined.
Fo high alues o β, ixed pa in RPP is highe han ixed pa in CPP. In pa icula ,
17
aI
c0
0.000
0.005
0.010
0.015
0.020
a
500
520
540
560
580
600
620
Fixed Pa
(a) β= 0.25
aI
c0
0.000
0.005
0.010
0.015
0.020
a
500
520
540
560
580
600
620
Fixed Pa
(b) β= 0.5
aI
c0
0.000
0.005
0.010
0.015
0.020
a
500
520
540
560
580
600
620
Fixed Pa
(c) β= 0.75
c0
0.000
0.005
0.010
0.015
0.020
a
500
520
540
560
580
600
620
Fixed Pa
(d) β= 1
Figu e 4: Fixed pa F. Pa ame e alues: c0= 0.01, c= 0.02, = 1500, λ= 0.002,
η= 2, = 0 and 0= 750.
BaK de e mines highe ixed ee han any o he alue o he access cha ge. The eason is
ha , when access cha ge is below cos , calls las mo e, he e o e he consume s’ su plus
ha ne wo ks can ex ac is highe . This coincides wi h many empi ical obse a ions. Fo
ins ance, O com (2009, pag. 37) expec s:
High e mina ion a es end o lead o a e ail p ice s uc u e wi h ela i ely
high o -ne call cha ges (since ope a o s ‘co e ’ hei wholesale cos o each
minu e o a call wi h a co esponding e ail cha ge) and lowe subsc ip ion
cha ges (since subsc ibe s gene a e incoming calls ha p o ide call e mina ion
e enue). [. . . ] Equally, i e mina ion a es a e low, consume s will end o
ace highe subsc ip ion ees bu lowe o no cha ges o make (o ecei e) calls.
Ma ke pene a ion. Fig. 5 illus a es ha he e is no a clea ela ionship be ween
ma ke pene a ion in he wo egimes. Fo low alues o ecei e ex e nali y, he e a e
alues o access cha ge such ha pene a ion is highe in CPP egimes. Con e sely, o
18
high ecei e ex e nali y, RPP egimes p esen a high numbe o subsc ibe s. This inde e -
minacy is also p esen in empi ical e idence: on he one hand Li lechild (2006) shows how
CPP a e deno ed by highe ma ke pene a ion, on he o he hand Analysis Mason (2008)
s a es ha ac ual da a mis ep esen ue alues o pene a ion by o e es ima ing pene a-
ion in CPP coun ies. Mo eo e , high pene a ion is explained h ough he highe su plus
he consume s ecei e. Once again in RPP we ha e he highes pene a ion a a=aI.
aI
c0
0.000
0.005
0.010
0.015
0.020
a
3
4
5
6
7
8
Subsc ibe s
(a) β= 0.25
aI
c0
0.000
0.005
0.010
0.015
0.020
a
3
4
5
6
7
8
Subsc ibe s
(b) β= 0.5
aI
c0
0.000
0.005
0.010
0.015
0.020
a
3
4
5
6
7
8
Subsc ibe s
(c) β= 0.75
c0
0.000
0.005
0.010
0.015
0.020
a
3
4
5
6
7
8
Subsc ibe s
(d) β= 1
Figu e 5: Ma ke pene a ion N. Pa ame e alues: c0= 0.01, c= 0.02, = 1500,
λ= 0.002, η= 2, = 0 and 0= 750.
G aphics show, once again, ha RPP egimes a e mo e sensible o a ia ions o he
pe cei ed ex e nali y: pene a ion is inc easing in β.
19
4.1 Wel a e analysis
We compa e he wel a e in he wo egimes in Fig. 6. To al wel a e is gi en by a weigh ed
sum o consume s su plus and indus y p o i s.14 As i is clea , he highes wel a e in
RPP is a ained a a=aI. A his alue o he access p ice, consume su plus o a call is
maximized and he ne wo k can ob ain he highes p o i s by ex ac ing i . In CPP he
highes wel a e is associa ed o alues o he access p ice close o he e mina ion cos .
aI
c0
0.000
0.005
0.010
0.015
0.020
a
2000
4000
6000
8000
10000
12000
14000
Wel a e
(a) β= 0.25
aI
c0
0.000
0.005
0.010
0.015
0.020
a
2000
4000
6000
8000
10000
12000
14000
Wel a e
(b) β= 0.5
aI
c0
0.000
0.005
0.010
0.015
0.020
a
2000
4000
6000
8000
10000
12000
14000
Wel a e
(c) β= 0.75
c0
0.000
0.005
0.010
0.015
0.020
a
2000
4000
6000
8000
10000
12000
14000
Wel a e
(d) β= 1
Figu e 6: To al wel a e W. Pa ame e alues: c0= 0.01, c= 0.02, = 1500, λ= 0.002,
η= 2, = 0 and 0= 750.
No ice ha as he ecei e ex e nali y inc eases, he wel a e is ge ing highe in RPP
14The consume su plus is gi en by he ne su plus consume s pe cei e in equilib ium acco ding wi h
equa ion (4) minus he o al amoun o he anspo a ion cos s:
CS pp =“ 0+N pp(U pp +˜
U pp −cD pp)−F pp”N pp −"„N pp −1
2«2
+1
4# ;
CScpp =“ 0+Ncpp(Ucpp +˜
Ucpp −pcppDcpp)−Fcpp”Ncpp −"„Ncpp −1
2«2
+1
4# .
20
egimes. This ac ema ks once again he impo ance o he egula o o ha ing a e y
p ecise knowledge o he alues o βwhen choosing he access p ice: e y low alues o a
(accompanied by a RPP egime) a e socially op imal only i he ecei ing ex e nali y is
high. The Eu opean Commission (2008) ends up o he same conclusion:
RPP migh no be e icien i he calling pa y alues he call highly bu he
called pa y does no and, as a esul , an e icien call migh no be comple ed.
The e e se issue may a ise in he CPP sys em, whe e an e icien call may no
be ini ia ed e en i he called pa y alues i highly bu he calling pa y does
no .
Indeed, i a egula o conside s ha in i s coun y he ex e nali y is e y low BaK is no
he wel a e maximizing policy.
Finally, assigning di e en weigh s o consume s su plus and indus y p o i s, esul s
do no change quali a i ely.
5 Conclusions
Regula o y au ho i ies a e conce ned abou educing mobile e mina ion a es bu he e
is a lack o heo e ical analysis ha could gi e hem hin s abou he consequences o such
a policy.
The Eu opean Commission (2008, 2009) p oposed a d as ic educ ion o he mobile
e mina ion a es du ing he nex yea s. This, acco ding o empi ical e idence and compa-
nies’ p e isions, would imply o cha ge consume s o ecei ing calls in o de o co e he
e mina ion cos o a call: he Eu opean Commission (2008, pag. 26) no iced ha “RPP
may e ol e a e a educ ion o he egula ed e mina ion cha ge o as a esponse o a Bill
and Keep sys em”. O com (2005) wa ned ha RPP egimes could ind he opposi ion o
consume s who do no wan o be cha ged o incoming calls.
In ou pape we p o ide a heo e ical amewo k ha allows o compa e he wo a i
egimes. We con i m he ela ionship be ween in e connec ion a angemen s and e ail
p ice s uc u e. I u ns ou ha i does no exis one a i egime supe io o he o he
o he in e ms o e ail p ices, usage, ma ke pene a ion and o e all wel a e o all alues
o he access p ice.
Using ealis ic alues o he indus y pa ame e s, we ind ou ha he le el o he call
ex e nali y is c ucial. When i akes high alues, ma ke pene a ion and o al wel a e a e
highe in a RPP egime wi h access cha ges close o ze o. This sugges s ha a BaK policy
(which esul s in he adop ion o a RPP egime) should be implemen ed only once he
p esence o a high call ex e nali y is p o en. O he wise access p icing a he e mina ion
21

cos would be a be e policy.
Up o ou knowledge, he e a e no es ima es o he call ex e nali ies. On he one hand, he
Body o Eu opean Regula o s o Elec onic Communica ions (BEREC (2010b)) poin ed
ou ha i seems easonable o assume ha he u ili y o he ecei e is lowe han ha
o he calle bu ha he di e ence is no e y signi ican . On he o he hand, in BEREC
(2010a) se e al phone companies claim ha he call ex e nali ies a e e y low o e en
equal o ze o.
A P oo s
P oo o P oposi ion 3.1 To ind he usage p ices we maximize p o i s wi h espec
o piand ikeeping ma ke sha e nicons an :
max
pi, i
πi
s. . pi, i≥0
We look o he in e io solu ions whe e pi, i>0. Fo a gi en ni, he i s o de de i a i e
o πiwi h espec o piwhen = i= jis:
q′[1 −F( −βpi)]{(ni+nj)(u′−c)−nj(a−c0) + ni(˜u′+E[ε|ε⩾ −βpi])
−ni
1
1 + 2 λ(˜u′+E[ε|ε⩾ −βpi]− )}= 0.(11)
Simila ly, o a gi en ni, he i s o de de i a i e wi h espec o iwhen p=pi=pjis:
ni(u′−c) + nj(a−c0) + (ni+nj)˜u′+ni
1
1 + 2 λ(u′−p) + E[εq′|ε⩽ i−βp]
E[q′|ε⩽ i−βp]= 0.(12)
As he noise anishes, when he calle and he ecei e wan o hang up a he same
ime we ha e ha u′=pand ˜u′= . In a symme ic equilib ium he i s o de condi ions
u n ou o be:
p= (c− ) + 1
2(c+a−c0−c+ )
= (c0−a) + 1
2(c−p−c0+a).
No ice ha bo h condi ions hold o p=c+a−c0and =c0−a. To ind he ixed pa
22
o he wo-pa a i , we de i e p o i s wi h espec o Fi:
∂πi
∂Fi
=∂ni
∂Fihni(pi−c)D(pi, i) + nj(pi−c−(a−c0))D(pi, j) + nj(a−c0)D(pj, i)
+ iniD(pi, i) + njD(pj, i)+Fi− i
+nih∂ni
∂Fi
(pi−c)D(pi, i) + ∂nj
∂Fi
(pi−c−(a−c0))D(pi, j) + ∂nj
∂Fi
(a−c0)D(pj, i)
+ i∂ni
∂Fi
D(pi, i) + ∂nj
∂Fi
D(pj, i)+ 1i
Using equilib ium p ices:
∂πi
∂Fi
=∂ni
∂Fihni(pi−c)D(pi, i) + nj(a−c0)D(pj, i)
+ iniD(pi, i) + njD(pj, i)+Fi− i
+nih∂ni
∂Fi
(pi−c)D(pi, i) + ∂nj
∂Fi
(a−c0)D(pj, i)
+ i∂ni
∂Fi
D(pi, i) + ∂nj
∂Fi
D(pj, i)+ 1i
=∂ni
∂FihFi− i+ni= 0
The e o e he ixed pa is:
Fi= −ni
∂ni
∂Fi
(13)
Combining (4) wi h (6) we ind he o al size o he ma ke Nand he numbe o consume s
ni: We ob ain:
N=1−λ(Fi+Fj−2 0)
1−2λ(U+˜
U−cD)and
ni=N
2+(Fj−Fi)(1 + λ )
2 (14)
Le us w i e he ma ke size as ollows:
N=1−λ(Fi+Fj−2 0)
γ(15)
whe e γ(a)≡1−2λ(U pp +˜
U pp −cD pp). The de i a i e o he ma ke sha e o ne wo k
iwi h espec o Fiis:
∂ni
∂Fi
=1
2h∂N
∂Fi
−1 + λ
i
=−1
2
λ +γ(1 + λ )
γ (<0) (16)
23
Subs i u ing (14) and (15) in o (13) and looking o he symme ic equilib ium, we ha e:
Fi= +N
2
2γ
λ +γ(1 + λ ).
Sol ing o Fwe ob ain:
F= + φ
γ+ (3 + γ)λ .
P oo o Lemma 3.1 Remembe ha γ(a)≡1−2λ(U pp +˜
U pp −cD pp). I s de i a i e
is:
∂γ
∂a =−2λh∂U
∂a +∂˜
U
∂a −c∂D
∂a i.
Le us i s compu e he de i a i e o he olume o calls wi h espec o he access p ice.
∂D
∂a =∂D
∂p
∂p
∂a +∂D
∂
∂
∂a
whe e15
∂D
∂p =∂F( −βp)
∂p βq(p) + [1 −F( −βp)]q′+q(p) ( −βp)(−β) = [1 −F( −βp)]q′
∂D
∂ =− ( −βp)q(p) + q(p) ( −βp) + 1
βZ −βp
¯
ε
q′ (ε)dε
=1
βEhq′ε≤ −βpiF( −βp).
Hence, we ha e
∂D
∂a =h1−F( −βp)iq′−1
βEhq′ε≤ −βpiF( −βp).
The de i a i e o he u ili y de i ed by making calls wi h espec o he access p ice is:
∂U
∂a =∂U
∂p
∂p
∂a +∂U
∂
∂
∂a
whe e
∂U
∂p =∂F( −βp)
∂p βu(q) + [1 −F( −βp)]u′(q)q′+u(q) ( −βp)(−β)
=[1 −F( −βp)]u′(q)q′
∂U
∂ =−F( −βp)
∂ u(q) + u(q) ( −βp) + 1
βZ −βp
¯
ε
u′(q)q′ (ε)dε
=1
βEhu′q′ε≤ −βpiF( −βp).
15He eina e q′<0 deno es he de i a i e o he lengh o a call wi h espec o he usage p ice.
24
Hence, we ha e
∂U
∂a =h1−F( −βp)iu′q′−1
βEhu′q′ε≤ −βpiF( −βp).
The de i a i e o he u ili y de i ed by ecei ing calls wi h espec o he access p ice is:
∂˜
U
∂a =∂˜
U
∂p
∂p
∂a +∂˜
U
∂
∂
∂a
whe e
∂˜
U
∂p =˜u′q′[1 −F( j−βpi)] + β˜u(q(pi)) ( j−βpi) + q′[1 −F( j−βpj)] E[ε|ε≥ j−βpi]
+βq(pi)( j−βpi) ( j−βpi)−β˜u(q(pi)) ( j−βpi)−βq(pi)( j−βpi) ( j−βpi)
=˜u′+Ehεε≥ −βpih1−F( −βp)iq′
∂˜
U
∂ =−F( −βp)
∂ ˜u(q) + q ( −βp)( −βp) + ˜u(q) ( −βp) + 1
βZ −βp
¯
ε
˜u′(q)q′ (ε)dε
+ ( −βp)q(p) ( −βp) + 1
βZ −βp
¯
ε
q′ε (ε)dε
=1
βEhq′(˜u′+ε)ε≤ −βpiF( −βp).
Hence, we ha e
∂˜
U
∂a =˜u+Ehεε≥ −βpih1−F( −βp)iq′−1
βEhq′(˜u′+ε)ε≤ −βpiF( −βp).
Hence, he de i a i e o γ(a) is:
∂γ(a)
∂a = 2λn1
βF( −βp)E[(u′(q) + ˜u′(q) + ε−c)q′|ε≤ −βp]
+h1−F( −βp)ihc−u′(q)−˜u′(q)−E[ε|ε≥ −βp]iq′o.
As he noise anishes we ge :
∂γ(a)
∂a = 2λn1
βF( −βp)hu′(q) + ˜u′(q)−ciq′−h1−F( −βp)ihu′(q)−˜u′(q)−ciq′o.
No ice ha when a > aI(a < aI) he calle ( he ecei e ) wan s o hang up i s and
he e o e we ha e ˜u′(q)> (u′(q)> p). This implies ha u′(q) + ˜u′(q)−c > 0. Mo eo e
emembe ha F( −βp) deno es he p obabili y ha he ecei e hang up i s : as he
noise ends o ze o his p obabili y is equal o 1 in ecei e so e eign y and equal o 0 in
consume so e eign y. Finally we ha e:
∂γ
∂a =




2λ
βhu′(q) + ˜u′(q)−ciq′<0 i a < aI;
−2λhu′(q) + ˜u′(q)−ciq′>0 i a > aI.
25
Sama aji a, R. & Melody, W. H. (2000). B ie ing pape . In Fixed-Mobile In e connec ion
Wo kshop. a ailable a h p://www.i u.in /osg/spu/ni/ mi/wo kshop/.
32