Market Expansion and Elasticity Improvement as Complementary Marketing Activities

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 This Ve sion is a ailable a : h ps://hdl.handle.ne /10419/159311 S anda d-Nu zungsbedingungen: Die Dokumen e au EconS o dü en zu eigenen wissenscha lichen Zwecken und zum P i a geb auch gespeiche und kopie we den. Sie dü en die Dokumen e nich ü ö en liche ode komme zielle Zwecke e iel äl igen, ö en lich auss ellen, ö en lich zugänglich machen, e eiben ode ande wei ig nu zen. So e n die Ve asse die Dokumen e un e Open-Con en -Lizenzen (insbesonde e CC-Lizenzen) zu Ve ügung ges ell haben soll en, gel en abweichend on diesen Nu zungsbedingungen die in de do genann en Lizenz gewäh en Nu zungs ech e. Te ms o use: Documen s in EconS o may be sa ed and copied o you pe sonal and schola ly pu poses. You a e no o copy documen s o public o comme cial pu poses, o exhibi he documen s publicly, o make hem publicly a ailable on he in e ne , o o dis ibu e o o he wise use he documen s in public. I he documen s ha e been made a ailable unde an Open Con en Licence (especially C ea i e Commons Licences), you may exe cise u he usage igh s as speci ied in he indica ed licence. h ps://c ea i ecommons.o g/licenses/by/3.0/ 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