Man o ani, And ea; Ami , Rabah
Wo king Pape
Ma ke Expansion and Elas ici y Imp o emen as
Complemen a y Ma ke ing Ac i i ies
Quade ni - Wo king Pape DSE, No. 470
P o ided in Coope a ion wi h:
Uni e si y o Bologna, Depa men o Economics
Sugges ed Ci a ion: Man o ani, And ea; Ami , Rabah (2003) : Ma ke Expansion and Elas ici y
Imp o emen as Complemen a y Ma ke ing Ac i i ies, Quade ni - Wo king Pape DSE, No. 470,
Alma Ma e S udio um - Uni e si à di Bologna, Dipa imen o di Scienze Economiche (DSE), Bologna,
h ps://doi.o g/10.6092/unibo/amsac a/4824
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Ma ke Expansion and Elas ici y Imp o emen as
Complemen a y Ma ke ing Ac i i ies
Rabah Ami ∗and And ea Man o ani†
Ap il 24, 2003
Abs ac
Conside a ma ke ing di ision o a monopoly i m ha aces wo ma ke ing
op ions: Ma ke enla gemen and elas ici y imp o emen . These op ions a e
concei ed in e ms o he a ge o he i m’s ad e ising campaigns: Po en ial
new consume s e sus exis ing consume s.
Using a CES demand unc ion in a simple model, we demons a e ha
he wo ac i i ies a e complemen a y, so ha o some cos con igu a ions, he
i m will ind i p o i able o implemen he wo op ions oge he when ei he
op ion alone would esul in a loss. This calls o he ma ke ing di ision o be
in eg a ed, a he han decen alized.
JEL classi ica ion:L12, M37, O32.
Keywo ds: Complemen a i y, ad e ising, i m o ganiza ion.
∗CORE, 34 Voie du Roman Pays, 1348, Lou ain-la-Neu e, Belgium. (Email:
[email p o ec ed]e).
†CORE, 34 Voie du Roman Pays, 1348, Lou ain-la-Neu e, Belgium and Depa men o Eco-
nomics, Uni e si y o Bologna, I aly (E-mail: man o [email p o ec ed]e).
1
1 In oduc ion
The concep o economic complemen a i y, ini ially in oduced by Edgewo h and u -
he de eloped as pa o ea ly mode n economic heo y by many pionee ing schola s
such as Samuelson (1974), has ecen ly ecei ed enewed a en ion in he managemen
science/ope a ions esea ch li e a u e h ough he wo k o Topkis (1978, 1998), which
ga e i i s mode n elegan and uni ied ma hema ical s uc u e. Mo e ecen ly, he
opic esu aced again in economics, eme ging as a leading heme o economic esea ch
p o iding he ideal me hodology o he s udy o games wi h s a egic complemen a -
i ies and hei use in indus ial economics (Vi es, 1990; Milg om and Robe s, 1990
and Ami , 1996) and o compa a i e s a ics analysis (Milg om and Shannon, 1994).
Ano he majo sphe e whe e he mode n concep o economic complemen a i y
has p o ed e ile and inspi ing is in he s udy o in e connec ed subsy ems linked
by complemen a i y ela ionships. This s and comp ises schola ly wo k in social sci-
ences, b oadly cons ued, and includes he heo y o he i m (Milg om and Robe s,
1995), he eme gence o mode n manu ac u ing (Milg om and Robe s, 1990), and he
wholis ic app oach o socio-economic sys ems along many in e - ela ed dimensions,
including economic, social, inancial, and his o ical ac o s (Hall and Soskice, 2001).
The main idea ha ies oge he he o he wise dispa a e s udies ha o m he la e
s and is ha , in he p esence o complemen a i ies linking he a ious subsys ems o
a global sys em, a sepa a e s udy o any one subsys em alone, ce e is pa ibus, is likely
o be subs an ially off he ma k in i s key conclusions, simply due o i s igno ance o
he unde lying complemen a i y ela ionships1.
1Fo ins ance, one canno simply compa e he inancial sys ems o he Uni ed S a es and Ge many
in isola ion om hei o e all socio-economic con ex , and conclude ha one o hem is supe io
o he o he . Ins ead, each o he sys ems is embedded in a much la ge whole h ough a web o
complemen a i y ela ionships ha ha e di ec impac on i s pe o mance. As a esul , each o he
2
The p esen s udy is an a emp o apply his undamen al bu simple idea o one
o he main unc ions o he i m: Ma ke ing/p oduc de elopmen 2.Ou s a ing
poin is hewell-knownmodelo Dixi andNo man(1978),whoe alua ed hesocial
desi abili y o ad e izing. In hei model, a i m acing an isoelas ic demand cu e
can engage in ad e izing ac i i y as ollows. I can make one ype o ad e izing
expendi u e ha has wo somewha in e - ela ed effec s: Ma ke expansion o an
upwa d shi in he demand cu e and elas ici y imp o emen 3.The o me effec
e lec s any a emp o each ou o new po en ial consume s while he la e aims a
inc easing exis ing consume s’ willingness o pay o he p oduc a hand. Bo h effec s
maybeachie edin he o mo in o ma i e ad e izing, which p o ides in o ma ion
abou he exis ence o po en ial quali y o a p oduc , o in he o m o pe suasi e
ad e izing, which aims a con incing he consume , in one way o ano he , ha wha
he eally wan s is he ad e ized b and. As o elas ici y imp o emen , some ypes
o ad e izing could educe p oduc subs i u abili y o a pa icula b and, and hus
lowe i s elas ici y o demand. This is ue in pa icula o pe suasi e ad e izing,
which in some cases c ea es a kind o pe cei ed p oduc diffe en ia ion ha does no
co espond o a eal diffe ence in he p oduc ’s pe o mance o cha ac e is ics4.
We modi y he Dixi and No man model inso a as we conside he i m’s o e all
wo sys ems is p obably be e han he o he in e ms o i ing well wi hin i s own whole.
2In a simila ein, he e a e some s udies dealing wi h he complemen a i y be ween p ocess and
p oduc inno a ion o a i m, including A hey and Schmu zle (1995), Adne and Le in hal (2001)
and Lin and Saggi (2002).
3Fo a discussion o he heo ies o ad e izing and he e idence o i s use by i ms, see Mans ield
(1996); Pepall, Richa ds and No man (1999, Ch 10); F iedman, 1983; and Ma in, (2001, Ch. 6).
4In he ma ke ing li e a u e, he e is an ex ensi e empi ical s and aiming a ca ego izing ads in
he a ious media acco ding o he numbe o in o ma ion ”cues” con ained in hem. The o e all
conlcusion is ha ads con ain li le ac ual in o ma ion ha would use ully guide consume s’ pu chase
decisions. See e.g. Resnik and S e n, (1997) and Abe na hy and F anke (1996).
3
ma ke ing ac i i y as consis ing o wo ap io iindependen ac i i ies, each con-
olling one o he a o emen ioned effec s sepa a ely. This di ision es s hus un-
damen ally on whe he a pa icula ad e izing campaign is aimed a new po en ial
consume s o a exis ing consume s. Ou objec i e is o es ablish in a e y simple
amewo k he complemen a i y o he wo ac i i ies, om he poin o iew o he
ma ke ing di ision o he i m, he eby jus i ying he cen aliza ion o ma ke ing ac-
i i ies wi hin he i m. To his end, we assume ha he monopolis has a i s disposal
h ee diffe en ma ke ing scena ios: (i) ma ke expansion alone, (ii) demand elas ic-
i y imp o emen alone, (iii) bo h goals simul aneously. Fo he sake o simplici y,
he wo ac i i ies a e desc ibed in he mos elemen a y manne possible ha allows
us o make ou poin : By expanding a ixed ou lay, he i m will be able o achie e
a ixed shi in he cha ac e is ic o in e es , o each o he wo op ions.
Fo he modi ied Dixi and No man model, we es ablish he simple ac ha
ma ke enla gemen is complemen a y o elas ici y imp o emen , when bo h op ions
a e modelled in he elemen a y bina y manne desc ibed abo e. As a consequence,
he e is a egion o in e media e ixed cos le els o he wo sepa a e op ions such
ha nei he o hem alone is p o i able while he simul aneous implemen a ion o
bo h is p o i able. Fu he mo e, we will show ha o such in e media e ixed cos
le els, he simul aneous in es men in bo h op ions gene a es a p o i ha ishighe
han he sum o he p o i gains de i ed om he wo sepa a e ac i i ies. I ollows
ha he ma ke ing di ision o such a i m should be no be emp ed o decen alize i s
ope a ions in i s a emp s o each ou o new consume s and o exis ing consume s.
Such decen aliza ion migh well miss ou on join ly p o i able ope a ions in cases
when each ope a ion alone is unp o i able.
4

2 The model
We conside a p o i maximizing monopolis ha aces a cons an ma ginal p oduc-
ion cos c. As o he demand side, we adop a modi ied e sion o Dixi and No man
(1978) using he isoelas ic demand unc ion:
Q(p)=ap
−b(1)
whe e a ep esen s a measu e o ma ke size and −bis he cons an elas ici y o
demand. We assume ha b>1, so ha he p o i -maximizing solu ion is in e io
(see below.)
The choice o such a demand unc ion is no innocuous. Fi s o all, he mul i-
plica i e o m is deemed mo e ealis ic han he linea addi i e o m in he manage ial
economics/ma ke ing li e a u e. Fu he mo e, such a demand can be easily linea ized
by aking loga i hms, so as o allow o i s pa ame e s o be easily es ima ed ia
s anda d eg ession.5Fo he p esen pape , as will be seen, i allows o a po en ial
sepa a ion be ween he wo ma ke ing effec s ha we wish o analyze.
The co esponding p o i unc ion is gi en by:
π(p)=(p−c)Q(p)(2)
F om he i s -o de condi ions, i is easily seen ha he op imal p ice is hen a
cons an ma k-up o e ma ginal cos , ano he a ac i e o his demand unc ion:
P∗=c
1−1/b.(3)
The le el o ma k-up hus depends in a simple way on he elas ici y o demand. By
plugging (3) in o (2) and ea anging, we ge an exp ession o he i m’s op imal
5See Mans ield (1996, Ch. 3) o an illus a i e discussion o he use ulness o he isoelas ic u ili y
unc ion in manage ial economics.
5
p o i :
π∗=ab−b(c
b−1)1−b(4)
The elas ici y o demand, de inedingene alas∈=p
q
dq
dp ,is he e equal o −b,a
nega i e cons an independen o he ou pu le el. I is well-known ha a monopolis
always p ices a a poin whe e |∈|>1, whence ou assump ion ha b>1. I is use ul
o no e ha an inc ease in demand elas ici y (co esponding o lowe ing he alue o
b)isp o i -imp o ing, i.e.:
∂π∗
∂b=−ab−b(c
b−1)1−b·log b+logµc
b−1¶¸<0.
I ollows ha he monopolis has an incen i e o inc ease demand elas ici y (i.e.
mo e ∈close o ze o), which is wha we e m elas ici y imp o emen h oughou he
p esen no e.
Wi hou aking cos s in o accoun , i is easy o see ha 6:
Lemma 1 Ma ke expansion and elas ici y imp o emen a e complemen a y ac i i-
ies.
6The o mal concep o complemen a i y in oked he e is due o Edgewo h, and co esponds o
he ma hema ical no ion o inc easing diffe ences o supe modula i y, which o a unc ion o wo
scala a iables is de ined as ollows. Fo all x0>xand y0>y,
F(x0,y0)+F(x, y)≥F(x, y0)+F(x0,y)
Fo a wice con inuously diffe en iable unc ion, his is equi alen o ∂2F(x, y)/∂x∂y≥0 o all
x, y. This makes i appa en ha he economic in e p e a ion o he complemen a i y be ween wo
a iables is ha ha ing mo e o ei he one inc eases he ma ginal e u ns o ha ing mo e o he
o he .
The ma hema ical analysis o complemen a i y, and i s a - eaching implica ions a e co e ed in
ull de ail in Topkis (1998).
6
P oo . As elas ici y imp o emen co esponds o a lowe b, we need only e i y
ha he c oss-pa ial de i a i e ∂2π∗
∂a∂bis <0(see Foo no e 5). Indeed, gi en ha
b>1,we ha e
∂2π∗
∂a∂b=−b−b(c
b−1)1−b·log b+logµc
b−1¶¸<0.
3 The Th ee Ma ke ing Op ions
Suppose ha he i m’s ma ke ing possibili ies can be desc ibed as ollows: Expend
esou ces on pu suing one o he ollowing h ee cou ses o ac ion.
(i) Op ion 1: Ma ke expansion alone.
(ii) Op ion 2: Elas ici y imp o emen alone.
(ii) Op ion 3: Bo h ma ke expansion and elas ici y imp o emen .
In he simples heo e ical amewo k, hese h ee op ions can be desc ibed as
ollows. Fo op ion 1, a ixed in es men o Kaenla ges he ma ke by a ixed amoun
∆a. Fo op ion 2, a ixed in es men in elas ici y imp o emen o Kbinc eases demand
elas ici y by ∆b,p o idedb−∆b>1.Fo op ion 3, he associa ed cos is simply he
sum o he sepa a e ixed cos s, o Ka+Kb.(We a e hus igno ing he possibili y ha
hecos o ealizing he wo ypeso ma ke ingcampaignsmaybeless han hesumo
he cos s o he wo sepa a e campaigns, i.e. ha he e is a cos complemen a i y, o
economies o scope, be ween hem. We will come back o his poin in he discussion
a he end o he pape .)
The p o i gain in case o ma ke expansion alone is gi en by (c . (4)):
πa=(a+∆a)b−b(c
b−1)1−b−Ka(5)
7
Ma ke expansion alone is p o i able i πa>π∗, which educes o he condi ion:
Ka<∆aΦ,c
Ka(6)
whe e Φ=b−b(c
b−1)1−b.
As o elas ici y imp o emen alone, he p o i gainisgi enby:
πb=a(b−∆b)−(b−∆b)(c
b−∆b−1)1−(b−∆b)−Kb(7)
Hence, op ion 2 is p o i able (i.e. πb>π∗)i
Kb<a(Ψ−Φ),c
Kb(8)
whe e Ψ=(b−∆b)−(b−∆b)(c
b−∆b−1)1−(b−∆b).
As o op ion 3, i he monopolis unde akes bo h op ions a he same ime, he
p o i will be equal o:
πa,b =(a+∆a)(b−∆b)−(b−∆b)(c
b−∆b−1)1−(b−∆b)−Ka−Kb(9)
Hence, op ion 3 is wo hwhile o he monopolis i
Ka+Kb<(a−∆a)Ψ−aΦ,d
Kab (10)
Akeyp ope yo hismodelisas ollows( hisiseasy o e i ycompu a ionally):
d
Kab >c
Ka+c
Kb(11)
The e a e h ee diffe en pa ame e con igu a ions o in e es o he analysis a
hand. The i s is he low cos s case, whe e bo h (6) and (8) hold. The monopolis
would hen implemen ei he op ion alone, as well as bo h op ions simul aneously.
The second is he high cos s case, whe e Ka+Kb>(a−∆a)Ψ−aΦ.In his
case, he monopolis would nei he implemen bo h op ions simul aneously, no ei he
op ion alone.
8