PRODUCT BUNDLING: THEORY AND APPLICATION

Transcription

1 PRODUCT BUNDLING: THEORY AND APPLICATION Bram Foubert September 999 Table of content. INTRODUCTION DEFINITIONS BASICS: THE ADAMS AND YELLEN MODEL MOTIVES PRICE DISCRIMINATION EPLOITING COST ADVANTAGES EPLOITING DEMAND COMPLEMENTARITIES INCREASING CUSTOMER VALUE STRATEGIC MOTIVES MOLDING PERCEPTIONS BUNDLING APPLIED OPTIMAL BUNDLE COMPOSITION AND PRICING MODEL DERIVATION OF RESERVATION PRICES DATA RESULTS LIMITATIONS AND FUTURE RESEARCH...44 REFERENCES...49 APPENDI : DERIVATION OF THE LOGISTIC RESERVATION PRICE DENSITY (5.7)...55 APPENDI 2: ETRACT FROM QUESTIONNAIRE...57 APPENDI 3: GAUSS-CODE...58 APPENDI 4: OUTPUT OF BELSLEY TEST FOR DATA OF UTILITY FUNCTION (5.4)...62

2 PRODUCT BUNDLING: THEORY AND APPLICATION Bram Foubert September 999 Abtract For more than three decade, microeconomit have been tudying the condition under which product bundling i a remunerative ale trategy. Only recently, bundling aroued the interet of marketing academic. Until now, no eriou attempt have been made to integrate the exiting reearch tream in the bundling literature. A firt merit of thi paper i the integration of the exiting microeconomic and marketing literature on product bundling in a comprehenive framework, which allow u to point out the lacuna. It turn out that little ha been aid about the actual implementation of a bundling trategy. One of the hardly addreed iue i the derivation of bundle reervation price, which are indipenable when determining the optimal bundle compoition and price. Therefore, a a econd merit, we preent a new method to compute bundle reervation price on the bai of paired comparion choice data and the latent cla binomial logit methodology. We then apply our method to the cae of multiple textbook bundle and ue an exiting LP bundling procedure to compute the optimal bundle compoition and price. Key word: Product Bundling, Optimal Bundle Compoition, Pricing, Linear Programming, Reervation Price, Conjoint Analyi, Logit Analyi, Latent Cla Etimation I wih to thank Wout Dullaert, Katia Campo, Sigrid De Wever, Lieje De Boeck, El Gijbrecht, Tom Gooen, Patricia Niol, Bart Van de Wielle, Walter van Waterchoot, Frank Verboven and Marcel Weverbergh for their help and comment.

3 . Introduction Often product or ervice are old in package: a viit to the zoo i tied to a train journey, ubcription TV channel are offered in modulated bundle (cf. Chae, 992), financial intitution, legally or not, ell tie-in of mortgage and life policie. And jut like many other (fat-food) retaurant, McDonald entice it cutomer with complete menu, compoed of burger, frie and oft drink. In fact a bicycle could be interpreted a a bundle of aembled part, with maybe the mot important component the aembly itelf. The lat 25 year the practice of what i called product bundling inpired a lot of microeconomit to develop model which explain the baic principle underlying bundling. Several reaon for the poible remunerativene of bundling were brought up. The variou model often involve very different explicit and implicit aumption, which reduce comparability. In 987 Guiltinan introduced bundling in the marketing literature a a trategic marketing tool. Although the marketing article on bundling after Guiltinan (987) are rather cant, they deal with very different apect. To our knowledge no attempt have been made to ituate the microeconomic and marketing article on product bundling in an integrating framework. Therefore, a a firt vantage point, we integrate the exiting reearch tream in the bundling literature and highlight the major gap to be bridged. It hould be treed, however, that it i not our intention to give an exhautive lit of article on bundling. From a methodological point of view, the optimal compoition and pricing of product bundle i a demanding job. Only a few author tackled thi iue. In thi paper we apply one of the exiting bundling procedure, which allow u to bring to life ome of the microeconomic principle. At the ame time, we come up with ome new idea, a econd vantage point of thi paper: we develop and apply a new method to infer bundle reervation price, a quinteential input when working out a bundling trategy. For thi 2

4 end, we ue the implicit bundle utility function, etimated with the latent cla binomial logit methodology, on the bai of paired comparion choice data. In ection 2 we define product bundling and it different face. Section 3 and 4 guide the reader through the literature on bundling. Section 3 expound the baic principle underlying bundling by mean of the Adam and Yellen model (976). In ection 4 we dicern a erie of poible motive for bundling, which at the ame time enable u to claify the exiting literature. Section 5 build on the idea preented in the previou ection, putting forward an LP-model for optimal bundle compoition and pricing, baed on Hanon and Martin (990). A method for etimating reervation price, which are ued in the LP-problem, i dealt with. We then apply thee technique to the cae of textbook package. Section 6 conclude thi paper, pointing out the limitation of our empirical reearch and the poibilitie for future reearch. 2. Definition In the literature there eem to be no generally accepted, clear-cut definition for product bundling. Jut in order to point out what will and what will not be the ubject of thi tudy, we define product bundling a the practice of elling two or more different product (or ervice) in a fixed proportion and at an explicit or implicit price (partly adopted from Carlton and Perloff, 994, p. 470). Product do not have to be pre-packed to make a bundle (which would be difficult for ervice anyway). It uffice that in ome way (explicitly or implicitly) a price for the combined product i et and communicated. The price information itelf may be bundled (price bundling) or unbundled. It i clear then that (product) bundling i a broader concept than price bundling. Offering a package at a ingle price i both product bundling 3

5 and price bundling. A promotion that allow a dicount on one product when a econd product i bought, i product bundling but no price bundling. Jut like Adam and Yellen (976) we ditinguih among two type of bundling, pure and mixed bundling. The former involve the availability of only the bundle while the latter refer to the availability of the bundle a well a one or more of the eparate component product. Although ometime bundling i ued a a ynonym for tie-in ale (cf. Warhit, 980, p. 80), we will clearly ditinguih among thee two notion. Following Carlton and Perloff (994, p. 470), bundling differ from tie-in ale 2 in that a tie-in doe not require product to be wrapped up in fixed proportion. A claic example of tie-in ale in variable proportion (requirement tie-in ale) i the IBM cae. In the 30 IBM obliged purchaer of tabulating machine to draw all punch-card, no matter what quantity, from IBM (Carlton and Perloff, 994, p. 470; Simon and Fanacht, 993, p. 405; Warhit, 980, pp. 8-82). Beide, a tie-in require that at leat one component cannot be purchaed eparately. A a conequence, a mixed bundling etting in which all component product are eparately available, i no tie-in. On the other hand, a bundling trategy in which at leat one component i not old apart, i a o called package tie-in ale (Carlton and Perloff, 994, p. 470). Again, in thi paper tie-in ale will be covered only a far a they involve package tie-in ale. The different notion and the link between them are ummarized in Exhibit. The difference between bundling and tie-in i epecially relevant from a legal point of view. In the US IBM wa prohibited to continue it tie-in arrangement in 936. And film ditributor had to abandon the practice of block booking of film (cf. infra) (Simon, 992, pp ; Simon and Fanacht, 993, p. 409). Belgian law impoe ome rigid retraint on the combined offer of product or ervice, which eem to correpond to what we defined a tie-in. The rule i that every uch offer i forbidden; it uffice that the offer can be perceived or experienced a a tie-in by the cutomer. Exception are made, among other, for product or ervice that belong together (De 2 For a pioneering article on tie-in, ee Burtein (960). 4

6 Vroede, 995, pp ). A brief analyi of cae law on thi ubject learnt that much depend on the actual circumtance (Judit data bae, 999/). tie-in ale bundling pure bundling mixed bundling : requirement tie-in : package tie-in Exhibit. Bundling and tie-in ale 3. Baic: the Adam and Yellen model In a eminal article, Adam and Yellen (976) introduced the baic bundling principle. Since their model wa ued a a tarting point in many ubequent paper, and ince it will be ued a a teppingtone in our empirical analyi, we dicu it here at length. Suppoe the following aumption hold: () A monopolit offer only two product: product and product 2. (2) The marginal cot (c and c 2 ) are contant with repect to output; the marginal cot of the bundle B i the um of the marginal cot of it component ( c B = c + c2 ); there are no fixed cot. 5

7 (3) Reervation price 3 for pecific conumer are unknown: perfect, or firt-degree, price dicrimination i therefore impoible. (4) Conumer reervation price (r and r 2 ) for a econd unit of the ame product are zero. The reervation price for both product bought imultaneouly ( of the reervation price for the eparate component ( r = r + r 2 ). +2 r +2 ), i the um (5) Zero aembly cot: a conumer can compoe the bundle him/herelf at no extra cot (Hanon and Martin, 990, p. 58), i.e. the conumer reervation price for the bundle ( r ) equal the reervation price for the elf-compoed bundle ( = ). B rb + 2 A a reult, in thi etting en r can be ued interchangeably. rb r + 2 (6) Free dipoal: a conumer can dipoe of an unwanted component at zero cot (Hanon and Martin, 990, p. 58). (7) Reale among conumer i nonexitent. (8) Conumer are urplu maximizing: conumer urplu i the difference between reervation price and product/bundle price; purchaing nothing yield zero conumer urplu. In the original article only aumption () to (4) are made explicit. Note that by impoing property (2), economie of cale and cope are aumed away 4. Aumption (4) exclude the poibility of complementaritie or ubtitutabilitie between bundle component. Aumption (5) in turn rule out the poibility that bundling in itelf offer extra aving on e.g. earch effort. Given aumption (4), aumption (6) i the ame a tating that all (component and bundle) reervation price hould be at leat zero 5. Conequently, every conumer can be ituated in the poitive quadrant by mean of hi/her reervation price, a i done for conumer in Exhibit 2. 3 Here the reervation price of a conumer for a good i the maximum amount of money that thi conumer would be willing to give up to get one unit of that good (Varian, 992, pp , 46). 4 A a conequence, if we normalized the reervation price for each product uch that r = r -c and r 2 = r 2 -c 2, we could carry out the analye with zero marginal cot and find the ame optimal trategy. 5 Actually, thi i not a tringent aumption ince, in thi etting, it i alway poible to normalize all reervation price uch that they become poitive. 6

8 r 2 A B r 2 p o 2 C D p o r r Exhibit 2. Pure component trategy Given the ditribution of both reervation price, the monopolit could et optimal price for both product (indicated a p o and p o 2 in Exhibit 2), orting the population into four egment. Conumer belonging to egment A only buy product 2 a their reervation price for product 2 i higher than p o 2 and their reervation price for product i lower than p o. For imilar reaon, conumer in egment B buy both product (like doe), thoe in egment C buy neither and thoe in egment D buy only product. In the context of bundling, thi trategy i often referred to a the pure component trategy. If the monopolit adopt the pure bundling trategy, he et an optimal price p B o for the bundle, given the ditribution of the bundle reervation price. In Exhibit 3 p B o i repreented by a traight line grouping all reervation price combination adding up to p B o. By aumption (4) all conumer ituated above thi line (egment A), buy the bundle a their purchae generate a poitive conumer urplu. Conumer in egment B o do not buy: their bundle reervation price are lower than p B. 7

9 r 2 p B o A B p B o Exhibit 3. Pure price bundling r In the cae of mixed bundling, the monopolit et optimal price for the eparate product and the bundle imultaneouly, uch that a demand exit for the bundle and at leat one component. Zero aembly cot (aumption (5)) force the optimal bundle price to be lower than the um of the eparate optimal product price, or, in other word and a hown in Exhibit 4, the line repreenting hould lie below the interection of o the line repreenting, repectively. Moreover, becaue of free dipoal o (aumption (6)), p B hould be higher than min{, }. Contraining the bundle price p p o 2 o between min{, } and + i called price ubadditivity (cf. infra). Note that when min{ p, }, the trategy adopted i no longer mixed bundling, but pure p B p 2 bundling. On the other hand, when +, mixed bundling boil down to the pure component trategy. In fact, it i eay to ee now that tarting from a mixed bundling o o ituation and letting p B, p and behave freely, would allow u to determine the overall optimal trategy. p o p o p o 2 p B p o 2 p p 2 p 2 p B o p o p o 2 Adopting mixed bundling, the monopolit divide the market into egment A, B, C and D. Conumer in egment A maximize their conumer urplu by purchaing only product 2. Conider for example conumer : buying product eparately i not an option 8

10 a reervation price for product i lower than p o. Buying the bundle would induce a poitive conumer urplu b. Purchaing product 2, on the other hand, yield urplu a, which i definitely higher than b. Given that a econd unit of the ame product i not needed (aumption 4), conumer only buy product 2. Analogou argument could be ued to how that conumer in egment D only buy product and that thoe in egment B are bundle buyer. Finally, it i obviou that egment C conit of non-buyer. r 2 A B p B o a. b p o 2 C p o p B o D r Exhibit 4. Mixed price bundling 4. Motive Bundling can be motivated by a number of different reaon. It hould be noted that thee reaon are not mutually excluive. Rather, it happen that one i a prerequiite for the other. A a matter of fact, one could even argue that many of thee motive are derivative of exactly the ame bundling phenomenon. We ucceively deal with bundling a a vehicle to purue price dicrimination (ection 4.), exploitation of cot ynergie (ection 4.2), exploitation of demand complementaritie (ection 4.3), enhancement of cutomer value (ection 4.4), leverage and product differentiation (ection 4.5) and manipulation of perception (ection 4.6). 9

11 4.. Price dicrimination It i beyond quetioning that in the microeconomic literature, price dicrimination i the motive for bundling that received mot attention and upport. Indeed, often bundling allow to extract more conumer urplu than were poible when elling the component product (only) eparately. Following Pigou (920), the type of price dicrimination decribed here i called econd-degree price dicrimination, a oppoed to firt-degree price dicrimination which allow the producer to extract the entire conumer urplu, imply by charging an individualized price which equal the conumer reervation price (Tirole, 988, p. 35). Stigler (963) i generally conidered a the firt articulating thi idea. In hi claic article on block booking, he analyze the movie ditributor practice of offering only a package of movie to exhibitor. Suppoe the ditributor of movie and Y, face the imple reervation price ditribution in Exhibit 5. Reervation price for Reervation price for Y Reervation price for bundle +Y Cinema Cinema Cinema Cinema Exhibit 5. A imple example of bundling with additive bundle reervation price Aume cot are zero and firt-degree price dicrimination i illegal. Charging the optimal price of 80 for film generate a profit of 60 (cinema 3 and 4 buy film ). Charging 85 for film Y yield an optimal profit of 70 (cinema and 2 buy film Y). In um, pricing the film eparately yield a profit of 330. If intead the movie ditributor opted for block booking and et the optimal price of 00, he would earn 400 (all cinema buy the bundle) and thu realize a higher profit. Thi example how that even without complementaritie (reervation price for the bundle are the um of the reervation price for the component product) and economie of cope (the marginal cot of the bundle i 0

12 the um of the marginal cot of the component) pure bundling allow further eroion of the total conumer urplu. Stigler note initiated a whole erie of article, trying to find out under which condition bundling could function a a remunerative price dicriminating device. Adam and Yellen (976) ( A&Y from here on) brought up the firt elaborate analyi. On the bai of the model preented in ection 3, they graphically explain the principle of thi type of bundling: which particular trategy - pure component trategy, pure bundling or mixed bundling - prevail in term of profitability, depend on the extent to which the bundling trategie approach firt-degree price dicrimination. Firt-degree price dicrimination alway atifie three condition. The firt one, full extraction, require the eller to extract the entire conumer urplu. By the econd condition, excluion, the monopolit doe not ell to individual with a reervation price below the marginal cot. Finally, incluion require the monopolit to ell to all individual with a reervation price above the marginal cot (A&Y, 976, p. 48). A a conequence, compliance with thee three condition determine the remunerativene of the bundling trategy. A&Y (976) proof that mixed bundling weakly dominate pure bundling, and even trictly dominate when pure bundling violate excluion 6. Thi turn the whole analyi into a comparion between the pure component trategy and mixed bundling. A&Y (976) conjecture that mixed bundling i better able to atify extraction and incluion imultaneouly when the reervation price are negatively correlated. A&Y tudy wa the bai for numerou heer theoretical a well a more applied paper. Schmalenee (982) alter aumption () of the original A&Y model, and conider a ingle-product monopolit who bundle hi product with another product produced in perfect competition. Schmalenee (982) firt demontrate that in thi etting pure bundling will never do better than pure component pricing. He then illutrate that mixed bundling i typically more profitable than the pure component trategy when the reervation price for the two good are negatively correlated. While 6 A&Y (976, p. 483, footnote) how that mixed bundling with bundle price P B and component price P = P B -c 2 and P 2 = P B c 2 will be at leat a profitable a pure bundling with bundle price P B.

13 A&Y (976) and Schmalenee (982) do not preuppoe any particular reervation price ditribution 7, Schmalenee (984) upplement the A&Y model with the aumption that reervation price follow a bivariate normal ditribution, inducing the component and bundle reervation price ditribution to be normal too. He rigorouly how that the prevalence of one of the trategie depend on the correlation between the reervation price, the tandardized difference between the average reervation price and the marginal cot (E(r j ) c j )/ σ (j =, 2), and the relation between thoe difference. The r j major implication i that the negative correlation between the reervation price i not a conditio ine qua non for mixed bundling to be more profitable than the pure component trategy. Olderog and Skiera (998) give further intuitive upport to Schmalenee finding. By altering the mean of the marginal (normal) reervation price ditribution and the correlation between the two reervation price, they imulate variou cenario, which demontrate that, a long a the tandardized difference between average reervation price and marginal cot are high enough, mixed bundling pay. Negatively correlated reervation price enhance thi profitability only to a leer degree. McAfee et al. (989) deal with the cae where reervation price follow any continuou joint ditribution, and derive trict condition for mixed bundling to be more profitable than the pure component trategy. From their analyi we even learn that mixed bundling trictly dominate pure component when reervation price are uncorrelated (!). Cairn (99) applie the A&Y model to the practice of bundling ticket for cultural event. He analyze two different mixed bundling trategie: the firt tie the availability of ticket for a high demand event 8 to the attendance at a low demand event, till allowing people to attend only the low demand event. In the econd trategy, the bundle a well a eparate ticket for both the high and the low demand event are available. The analyi differ from the one in A&Y (976) in that Cairn (99) account for the natural capacity contraint, typical of mot cultural event. However, Cairn (99, p. 83) draw more or le the ame general concluion regarding the reervation price ditribution. Lan and Kanafani (993) tudy park-and-hop program, which actually 7 Thi i the main reaon why mot of their concluion are rather tentative. 2

14 bundle parking ervice and hopping: viitor of a hopping center can make ue of the nearby parking facilitie at a dicount. The author adopt the A&Y model but in addition aume reervation price to follow a joint uniform ditribution. Under thee condition, it turn out that, in term of profit, mixed bundling hould be preferred to the pure component trategy. A rather limited number of article on product bundling motivated by the ame price dicrimination principle, ue model other than the A&Y model. Parouh and Pele (98) alter aumption (4) of the A&Y model, reckoning with trictly poitive reervation price for a econd unit of the ame commodity, which invalidate A&Y graphical analyi. A a reult, it can be more lucrative to bundle everal unit of the two component, yet till in a fixed proportion (an eential characteritic of a bundle). Parouh and Pele determine the optimal proportion in rather artificial circumtance 9 and derive ome ufficient condition for pure bundling to dominate the pure component trategy. On the bai of the A&Y-model, Hanon and Martin (990) develop an LPmodel for optimal bundle compoition and pricing when more than two component (and therefore everal bundle option) are involved. Thi model, which will be extenively dealt with in ection 5, at the ame time relaxe aumption (2) (abence of cope economie) and (4) (abence of complementaritie). Venkateh and Mahajan (993) tudy the impact on profit of a eaon ticket bundling a particular number of cultural event. Their model i particularly intereting in that it take into account the expected number of cultural event a conumer will attend. In fact, by reckoning with thi expected attendance, the author indirectly introduce demand interdependencie (ubtitutabilitie) in their model. Auming reervation price and expected attendance to be Weibull ditributed, Venkateh and Mahajan illutrate the optimality of mixed bundling on the bai of urvey data. Unlike Cairn (99), however, they do not include capacity contraint. Anari et al. (996) extend the model by Venkateh and Mahajan (993), determining endogenouly the number of cultural event compried in the eaon ticket. 8 I.e. for which people have high reervation price. 9 The author conider two egment of conumer. For each egment they preuppoe two linear demand curve (one for each product) of a very retrictive nature. 3

15 Moreover, they conider the poibility of offering everal eaon ticket, each bundling a different number of event 0. Again, mixed bundling i hown to be mot profitable. A a matter of fact, both Venkateh and Mahajan (993) and Anari et al. (996) implicitly illutrate that the ditinction between product bundling and multi-unit pricing i only a fuzzy one. Finally, Guiltinan (987) tranlate the A&Y model into more operational condition relating to the bundle and component (reervation) price, and reckoning with complementaritie and (exogenou) competitive price. Guiltinan in particular tree the importance of price egmentation, which i a natural conequence of the bundling proce: by elf-election, conumer ort themelve into different egment with different reervation price characteritic. A a reult, bundling allow a firm to implement three different trategie: cro-elling the bundle to thoe cutomer that ued to buy only one component, acquiition of conumer that ued to buy neither component or retention of thoe cutomer that ued to buy both component Exploiting cot advantage In the previou analyi it wa aumed that the marginal cot of a bundle wa equal to the um of the marginal cot of the component (aumption (2)). However, often economie of cope (due to aving in production, ditribution, tranaction and/or information on the part of the eller) offer an extra motive for bundling. It i intuitively clear that in thi cae bundling become an even more attractive trategy ince elling the bundle guarantee a higher profit margin than in the abence of economie of cope. It hould be noted, though, that part of thee cot advantage can alo be realized without bundling: if, in a particular time period, one conumer want only the firt component and another conumer only the econd component, both component can be produced (ditributed) imultaneouly, poibly implying cot ynergie. For implicity, we conider here (and in the ret of thi paper) thoe economie of cope which are realized only when the ame conumer i provided with both component imultaneouly. 0 Anari et al. (996, p. 89) call thi trategy amplified mixed bundling. 4

16 Although Eppen et al. (99, p. 8) illutrate the cope economie motive, and though Hanon and Martin (990) allow for cope economie in their optimal bundling model, to our knowledge, Chae (992) upplie the only rigorou analyi of cot ynergie in a bundling context. He conider a monopolit who incur a contant marginal ditribution cot c when a houehold ubcribe to at leat one of two TV-channel. Thi ituation i graphically depicted in Exhibit 6. Notice that thi i an extreme cae of cope economie for the cot of providing one houehold with both TV-channel i equal to the cot of providing only one TV-channel. r 2 o p B o p 2 c c o p o p r B Exhibit 6. Bundling and economie of cope Auming that reervation price follow a ymmetric, bivariate uniform ditribution, and repecting the other A&Y aumption, Chae then prove that mixed bundling i the profit maximizing trategy and compute the optimal price 2. In fact, in thee circumtance bundling by definition till function a a price dicriminating tool ince it Hanon and Martin (990, p. 65) provide an example howing that, when marginal cot are ubadditive, bundling may be even neceary in order to make poitive profit. 2 Apart from the profit maximizing objective, Chae alo conider a welfare maximizer and a profitcontrained (i.e. ubject to the contraint that the profit i nonnegative) welfare maximizer. 5

17 more completely complie with the price dicrimination condition than the pure component trategy 3. The difference between the preent ituation and the one decribed in ection 4. i that here the bundle remunerativene i no longer excluively attributable to the preference tructure Exploiting demand complementaritie Complementaritie induce a conumer to be willing to pay a higher price for both product than jut the um of the eparate reervation price, i.e. r (= r ) > r + r 2 (cf. aumption (4)). The preence of complementaritie invalidate the graphical A&Y model ince the preference tructure of a ingle conumer can no longer be decribed by two coordinate in the reervation price pace, unle +2 B can be written a a function of (r,r 2 ). From the previou ection, we know that thee complementaritie are no prerequiite for bundling to be remunerative. Yet, complementary component make profitable bundling a much impler tak (Paun, 993, p. 3; Lawle, 99, p. 27). Although complementaritie (and inter-product relationhip in general) can alo be exploited - to a certain extent - by optimal product line pricing (cf. Mulhern and Leone, 99) 4, often bundling i better able to do o thank to it price dicrimination characteritic. r +2 Balderton (956) ditinguihe two type of complementaritie (Mulhern and Leone, 99, p. 65). Ue complementarity i the enhancement of conumer level of atifaction when product are conumed together. Ue complementarity can refer to the functional relation between the product, but alo to the atifaction derived from buying everal 3 Chae alo introduce production cot: prior to the pricing deciion, the monopolit decide whether to produce only the firt channel at a ingle etup cot C, only the econd channel at a etup cot C 2, or both, at a etup cot C B (which can be lower than, equal to, or higher than the um of C and C 2 ). A a conequence, although mixed bundling i optimal once both channel are produced (i.e. when C B i a unk cot), it could be that offering only one channel i overall a more profitable trategy. 4 Mulhern and Leone (99) ue the term implicit bundling to denote product line pricing: a rather unfortunate choice, ince by no mean product line pricing implie price dicrimination, which i typical of product bundling. 6

18 product under one known brand name, or to the eae of obtaining after-ale upport from a ingle ource (Lawle, 99, p. 274). Purchae complementarity involve aving in time, effort and tranportation cot from purchaing product together (cf. Guiltinan, 987, p. 79). A a reult, one could regard all product available in one tore a complement. Anyway, note that buying the bundle i no prerequiite for conumer to realize whatever complementaritie: conumer can jut a well compoe the bundle themelve 5. Although ome attention ha been given to complementaritie in the tie-in literature (cf. Burtein, 960; Warhit, 980), which i partly relevant for product bundling, the iue remain to be fully explored in the bundling literature. Guiltinan (987) and Hanon and Martin (990) account for complementaritie (uperadditive bundle reervation price) in their repective model, but the mot compelling (and complex) analyi motivated by the preence of complementaritie i due to Teler (979). Teler aume that n conumer buy m component only in fixed proportion 6, that the n conumer-pecific proportion vector are no linear combination of each other, that cot ynergie are abent and that the eller ha a monopoly over at leat one component. He then prove that it i remunerative to compoe and price n cutomized bundle (poibly with everal unit of the ame component) in lieu of pricing the m eparate component Increaing cutomer value Until now, we aumed that a cutomer can compoe the bundle himelf at no extra cot, or, in other word, that the bundle offer no additional value above the value of the elfcompoed bundle (aumption (5)). Thi aumption may not alway be a realitic one: it could be that r B > r +2. Different ource of thi intrinic bundle value can be pointed out. By buying the bundle, a cutomer can ave on earch cot. Epecially in the beginning of the product life cycle, obtaining bundled product can be a cot aving 5 Albeit that bundling in itelf create de facto complementaritie between the bundled product, ince the product are bought together. 6 Thi mean that the component are perfect compliment, at conumer level. 7

19 alternative for the earch for further information on the eparate product (Lawle, 99, p. 27; Paun, 993, pp. 30, 32). Often the eller ha better expertie and information on what product work properly together (Eppen et al., 99, p. ) (cf. computer and peripheral). Eppen et al. (99, pp. -2) tate that, for new product, bundling help conumer undertand the full range of product and ervice benefit, which they call product definition bundling. In addition to aving on earch effort, bundle alo allow conumer to realize extra aving on tranaction cot (Lawle, 99, p. 274). Thi i epecially true for pre-packed bundle. Danby and Conrad (984) eem to be the only one who allow for thi additional bundle value in a formal analyi. By introducing a bundle reervation price function rb = b(r,r 2 ), they contruct a graphical, twodimenional model, comparable to the A&Y model. However, their concluion with repect to profit implication are trivial and/or intuitive. Among other thing they conclude that bundling i the preferred trategy when the bundle yield additional value (i.e. = b( r, r r + r = r + ). r B 2) Strategic motive In the trategic bundling literature, author eem to dicern two related bundle effect: extenion of market power (leverage) and product differentiation. The firt involve the penetration of a competitive market by bundling a monopolitically produced component with the component produced in the competitive market. Wherea Schmalenee (982) argue that bundling a monopolitically produced good with a good produced in perfect competition i no leverage 7, Carbajo et al. (990) how how a monopolit can extend hi market power (and enhance profit) by bundling hi product with ome other good produced in a duopolitic market. The author preume that reervation price are perfectly poitively correlated and uniformly ditributed, and repect the other relevant A&Y aumption. Under both Bertrand price and Cournot quantity competition, they 7 A wa mentioned in ection 4., Schmalenee firt prove that a monopolit will never chooe to tie in hi product with a product of a perfectly competitive indutry in a pure bundle. Schmalenee then argue that mixed bundling (the optimal trategy) hould not be conidered a leverage ince the monopolit i indifferent between producing the competitive product himelf and buying it at cot from the competitive indutry. 8

20 derive trict condition 8 for pure bundling (which dominate mixed bundling) to be remunerative. It turn out that, under Bertrand competition, both firm benefit from pure bundling. However, under Cournot competition, the profit of the non-bundling firm fall. Martin (999) preuppoe imple linear demand curve and Cournot-quantity etting duopolit, and retain the other A&Y aumption. He, too, find that the monopolit benefit from pure bundling, unlike the non-bundling firm. The econd trategic bundling implication i the differentiation of a good produced in a competitive market, by bundling it with another product. Chen (997) analyze a twotage game. In the firt tage, two firm decide imultaneouly what product to offer and which trategy (pure/mixed bundling, pure component) to implement. One component i produced in duopolitic competition, the other in perfect competition. In the econd tage, the firm et Bertrand-price for their product/bundle. Conumer reervation price can follow any continuou ditribution on a finite upport. Maintaining the other A&Y aumption, Chen then prove that pure bundling weakly dominate mixed bundling and that the Nah-equilibrium dictate one firm to offer the (pure) bundle and precribe the other to ell only the duopolitic product Molding perception Recent marketing literature on bundling particularly focue on the pychological rather than on the economic apect of bundling. While all previou motive conider each cutomer a a rational homo economicu, thi new reearch tream analyze the way price information i proceed in a bundle context and the way the bundle value and quality i perceived. A firt focal point in thi reearch tradition concern framing effect, or the impact of the preentation of the bundle price information on price perception. Under perfect rationality, a cutomer would be indifferent between e.g. ) buying product A and B together at $0 (price bundling), 2) buying A at $6 and B at $4 when A and B are bought 8 Thee condition relate to the (contant) marginal cot. 9

21 together, and 3) buying A at $0 and getting B for free (or vice vera). Alo, a cutomer would be indifferent between e.g. ) $2 off the bundle price, 2) $2 off the price of A when B i bought at the regular price (or vice vera), and 3) $ off the price of A and $ off the price of B when A and B are bought imultaneouly. In other word, under perfect rationality, conumer urplu, and therefore perceived price and price dicount, are uppoed to be additive and completely tranferable from one product to another (Yadav, 995, p. 207). Several author conider departure from thee (implicit) aumption. Some author refute the aumption that (perceived) price and price dicount of the eparate component can imply be added up to a ingle perceived price, repectively price dicount. Johnon et al. (999) apply Thaler mental accounting theory (985) to product bundling. Thi theory poit that egregated (monetary) gain x and y induce a higher value than the correponding integrated gain x + y (i.e., if v() i the value function, v(x) + v(y) > v(x + y)), and that egregated (monetary) loe -x and -y are perceived a le harmful when they are integrated into a ingle lo -x - y (i.e. v(-x) + v(-y) < v(-x - y)). A a reult, conumer prefer a ingle bundle price (conidered a a lo) to eparate product price and conider eparate dicount (conidered a gain) a more favorable than a ingle bundle dicount (Johnon et al., 999, pp ). Johnon et al. tet and confirm their hypothee in an experimental pure bundling deign, where the bundle conit of a baic model of a particular automobile and optional extra. Conumer evaluation of the bundle offer include atifaction with the offer, likelihood of recommending the offer to other people, and likelihood of (re)purchaing the bundle. Yadav and Monroe (993) draw on the ame mental accounting principle, though in a lightly different experimental etting. They conider a mixed bundling deign with a garment bag and a uitcae a component product. Dicount on the product, when bought eparately, a well a the extra dicount on the bundle differ acro the bundle/price-profile. The reult eem to indicate that conumer rate the tranaction value of an offer with egregated dicount (e.g. a $0 dicount on each eparate product and an extra $20 dicount on the bundle) higher than the tranaction value of the offer with correponding integrated bundle dicount (no dicount on the eparate product, a $40 dicount on the bundle price). Harlam et al. (995), too, focu on framing effect. In 20

22 an interactive computer experiment repondent were firt aked to enter their reervation price for 0 individual branded product (VCR, TV, watch, videotape, backpack, hampoo, conditioner, oap, chocolate and cookie). The computer program then preented two-component bundle at a egregated or integrated price. Price equaled the (um of the) correponding reervation price plu a premium or minu a dicount. The reult upport mental accounting inofar that integrated price information give rie to a higher purchae intent than egregated price information. However, the reult regarding the price premium and dicount go exactly in the oppoite direction. One of the theorie explaining thee finding, i Weber law, which implie that a large price change i more likely to be noticed than a mall price change. A a conequence, on the bai of thi law, one would opt for egregated price premium and integrated price dicount. One reaon for the failure of the mental accounting principle i that, in the experiment, neither premium nor dicount were highlighted a uch (Harlam et al., 995, p. 59). Yadav (995) quetion the perfect tranferability of conumer urplu from one bundle component to another. In particular, he examine whether conumer are indifferent between a dicount on one of two magazine, purchaed together, (a port magazine and an entertainment magazine) and a monetarily equivalent dicount on the other magazine. It turn out that dicount are more effective (in term of bundle utility and choice probability) when offered on a conumer preferred magazine. Yadav reult how that the preference heterogeneity, which underlie the ucce of price dicrimination, at the ame time influence the way price information hould be framed. Apart from the emantic effect of price information, the recent behavioritic marketing literature alo invetigate how bundle compoition affect the perceived bundle value. In a pure bundling experiment, where repondent evaluated bundle made up of a primary product and a free product (VCR + free videotape, repectively typewriter + free calculator), Gaeth et al. (990) find that bundle quality and uefulne perception are equal-weight-average of the eparate component perception. They alo demontrate that the freebie-equivalent-dicount (i.e. the dicount that would make conumer indifferent between the bundle and the primary product with that dicount) i higher than 2

23 the retail value of the free product, and increae with the quality of the free product and, to a leer extent, with the quality of the primary product. Further, Gaeth et al. how that bundle reervation price are influenced by the quality of the repective bundle component: for functionally related bundle (VCR + tape), for which overall uperadditivity could have been expected, a free low quality product trigger reervation price ubadditivity. For unrelated product (typewriter + calculator), a primary low quality product bundled with a free product of any quality induce uperadditivity. In the computer experiment mentioned above, Harlam et al. (995) find that, overall, functionally related product (e.g. hampoo + conditioner) imply a higher bundle purchae intent than monetarily equivalent unrelated product (e.g. hampoo + cookie). Summing up, one need little imagination to realize that ignoring perceptual effect could highly bia the alleged poitive impact of a bundling trategy. The other ide of the coin i that bundling can be an opportunity to mold favorable perception at a limited cot. From the above dicuion, it may eem that bundling only pay in term of profit. However, mot of the aforementioned article (except for thoe in ection 4.6) at leat uccinctly dwell on the poibly (!) favorable welfare implication. Yet, it i evident that the welfare maximizing trategy and price do not alway coincide with the profit optima. A a detailed analyi of the welfare implication i outide the cope of thi paper, the intereted reader i in particular referred to Anari et al. (996) who put forward compelling objective other than profit (or revenue) maximization. Exhibit 7 ytematically arrange the motive and the literature mentioned above. It hould be treed that thi claification doe not contain an exhautive lit of article on bundling. Our only intention wa to integrate the main reearch tream available in the bundling literature. Moreover, due to it inductive character, our framework i poibly conceptually incomplete. Yet, we are convinced that thi framework, together with our empirical reearch preented in the next ection, will enable u to touch the ore pot in the bundling literature. 22

24 Motive Author Demand ide characteritic Supply ide characteritic Component Demand Bundle Cot tructure Competitive preference interdependencie preference ituation Price dicrimination Stigler (963) - any dicrete r- ditribution - r for econd unit of ame component = 0 Adam and Yellen (976) Parouh and Pele (98) Schmalenee (982) Schmalenee (984) Guiltinan (987) McAfee et al. (989) Hanon and Martin (990) - any dicrete r- ditribution - r for econd unit of ame component = 0 imple linear demand curve - any dicrete r- ditribution - r for econd unit of ame component = 0 - normal r-ditribution - r for econd unit of ame component = 0 - any dicrete r- ditribution - r for econd unit of ame component = 0 - any continuou r- ditribution - r for econd unit of ame component = 0 - any dicrete r- ditribution - r for econd unit of ame component = 0 none none none none none complement none ubtitute/ complement no additional bundle value ( r = r +2 ) B no additional bundle value ( r = r +2 ) B no additional bundle value no additional bundle value ( r = r +2 ) B no additional bundle value ( r = r +2 ) B no additional bundle value ( r = r +2 ) B no additional bundle value ( r = r +2 ) B no additional bundle value NA no cale or cope economie no cale or cope economie no cale or cope economie no cale or cope economie no cale or cope economie no cale or cope economie no cale economie, cope economie poible monopoly for both component monopoly for both component monopoly for both component monopoly for one component, other component produced in perfect competition monopoly for both component duopoly for both component (without trategic interaction) monopoly for both component monopoly for all component Remark/application theoretical/empirical (pure bundling - two component - block booking of movie) theoretical (pure/mixed bundling - two component) theoretical (pure bundling - two component poibly everal unit of the ame component) theoretical (pure/mixed bundling - two component) theoretical (pure/mixed bundling - two component) theoretical (pure/mixed bundling - two component) theoretical (mixed bundling - two component) theoretical/ empirical (pure/mixed bundling - unlimited number of component - bundle of home ervice: ironing, hopping, etc.) Major finding intuitive upport for bundling to be remunerative when relative reervation price vary acro cutomer - Mixed bundling at leat weakly dominate pure bundling - Mixed bundling eem to dominate pure component when reervation price are negatively correlated - determination of the optimal bundle proportion - ufficient condition for pure bundling to dominate pure component - Pure component weakly dominate pure bundling. - Mixed bundling eem to dominate pure component when reervation price are negatively correlated. Correlation between reervation price, E r c (j =, 2) determine and ( ) j σ r j j optimal trategy. - derivation of condition (relating to bundle and component price and preference) for bundle to be effective - profitability conideration derivation of trict condition for mixed bundling to be more profitable than pure component mixed integer LP model for optimal bundle compoition and pricing 23

25 Motive Author Demand ide characteritic Supply ide characteritic Component Demand Bundle Cot tructure Competitive preference interdependencie preference ituation Price dicrimination (cont.) Exploiting cot advantage Exploiting complementaritie Cairn (99) - any dicrete r- ditribution - r for econd unit of ame component = 0 Lan and Kanafani (993) Venkatek and Mahajan (993) Anari et al. (996) Olderog and Skiera (998) - uniform r- ditribution - r for econd unit of ame component = 0 - Weibull r- ditribution - r for econd unit of ame component = 0 - Weibull r- ditribution - r for econd unit of ame component = 0 - normal r-ditribution - r for econd unit of ame component = 0 none none ubtitute ubtitute none no additional bundle value ( r = r +2 ) B no additional bundle value ( r = r +2 ) B no additional bundle value ( r = r +2 ) B no additional bundle value ( r = r +2 ) B no additional bundle value ( r = r +2 ) B NA no cale or cope economie only fixed cot only fixed cot no cale or cope economie monopoly for both component monopoly for both component monopoly for all component monopoly for all component monopoly for both component Remark/application theoretical (mixed bundling - two component: high demand event (with capacity contraint) and low demand event) theoretical/empirical (mixed bundling - two component park-andhop bundle) empirical (pure/mixed bundling eaon ticket for 0 event) empirical (pure/mixed bundling eaon ticket for variable number of performance) theoretical (pure/mixed bundling two component) Major finding W.r.t. mixed bundling, tying high demand event to low demand event: The more popular i the high demand event, the more likely revenue will fall. The le popular i the low demand event, the more likely revenue will rie. Mixed bundling dominate pure component. Mixed bundling i optimal trategy. - Derivation of optimal number of bundled event - Mixed bundling i optimal trategy. When ( ) E r j c j (j =, 2) are high enough, mixed bundling pay. cf. upra cf. upra cf. upra cf. upra cf. upra cf. upra cf. upra Hanon and Martin (990) Chae (992) - uniform r- ditribution - r for econd unit of ame component = 0 none Teler (979) linear demand curve complement (conumerpecific) Guiltinan (987) Hanon and Martin (990) no additional bundle value ( r = r +2 ) B - (conumerpecific) linear demand curve - no additional bundle value cope economie no cale or cope economie monopoly for both component monopoly for at leat one component theoretical (pure/mixed bundling two component bundle of ubcription TV channel) theoretical (pure bundling poibly with everal unit of ame component unlimited number of component) cf. upra cf. upra cf. upra cf. upra cf. upra cf. upra cf. upra cf. upra cf. upra cf. upra cf. upra cf. upra cf. upra cf. upra σ r j Mixed bundling i mot profitable trategy. Pure bundling (cutomized bundle) dominate pure component trategy. 24

26 Motive Author Demand ide characteritic Supply ide characteritic Component Demand Bundle Cot tructure Competitive preference interdependencie preference ituation Increaing cutomer value Strategic motive Molding perception Danby and Conrad (984) Carbajo et al. (990) - any continuou r- ditribution - r for econd unit of ame component = 0 - uniform r- ditribution - r for econd unit of ame component = 0 - r en r 2 perfectly poitively correlated Chen (997) - any continuou r- ditribution on finite upport - r for econd unit of ame component = 0 Martin (999) linear aggregated demand curve Gaeth et al. (990) Yadav and Monroe (993) Any NA none none none none complement additional bundle value poible, r B = b(r, r 2 ) no additional bundle value ( r = r ) B +2 no additional bundle value ( r = r ) B +2 no additional bundle value teted (ee Major finding) no cale or cope economie no cale or cope economie no cale or cope economie no cale or cope economie monopoly for both component monopoly for one component, duopoly for other component duopoly for one component, perfect competition for other component monopoly for one component, duopoly for other component Remark/application theoretical (pure/mixed bundling two component) theoretical (pure/mixed bundling two component) theoretical (pure/mixed bundling two component) theoretical (pure bundling two component) NA NA empirical (pure bundling - bundle compoed of VCR and tape, rep. typewriter and calculator) NA NA NA NA empirical (mixed bundling bundle of uitcae and garment bag) Major finding Bundling pay if b( r., r2 ) r + r2 = r Pure bundling (weakly) dominate mixed bundling for both firm. - derivation of trict condition (w.r.t. marginal cot) for (pure) bundling to be remunerative - Pure bundling (weakly) dominate mixed bundling for both firm. - Equilibrium: one firm bundle, other firm ell only duopolitic product. Bundling firm enhance it profit at the competitor expene. - Conumer evaluation of bundle quality and uefulne are equal-weightaverage of the component evaluation. - Free low quality product, bundled with functionally related product, induce r- ubadditivity. Free product, bundled with unrelated low quality product, induce r-uperadditivity. - Freebie-equivalent-dicount i higher than retail value of freebie. Conumer evaluation of bundle offer increae when dicount information i plit up into dicount on eparate product + extra dicount on bundle. 25