Bundled Discounts: Strategic Substitutes or Complements?

Transcription

1 Bundled Dicount: Strategic Subtitute or Complement? Duarte Brito y Univeridade Nova de Liboa and CEFGE-UE Helder Vaconcelo z Faculdade de Economia, Univeridade do Porto, CEF.UP and CEPR June 2, 24 btract Bundled dicount by pair of otherwie independent rm play an increaingly important role a a trategic tool in everal indutrie. Given that price of rm competing for the ame conumer are trategic complement, one would expect their dicount level alo to be trategic complement. However, in thi paper we how that under ome circumtance bundled dicount may be trategic ubtitute. Thi occur under vertically di erentiated product where a low quality pair of producer may indeed prefer to lower it dicount after an increae in the dicount o ered by a high quality pair of producer. Keyword: Bundled Dicount, Bilateral Bundling, Strategic Subtitute. JEL Clai cation: D43; L3; L4. Thi paper wa nanced by national fund from the FCT under project PTDC/EGE-ECO/558/29. y DCS, Faculdade de Ciência e Tecnologia da Univeridade Nova de Liboa, Quinta da Torre, Caparica, Portugal. dmb@fct.unl.pt. z Faculdade de Economia da Univeridade do Porto, Rua Dr. hvaconcelo@fep.up.pt Roberto Fria, Porto, Portugal.

2 Introduction When price are trategic complement, a i commonly accepted in the literature, one would expect that the bet repone of a given rm to an increae in a dicount o ered by a rival would be to increae it dicount a well. In general, common widom hold that [w]hether the competitive action i baed on price, comparion advertiing or coupon, a more aggreive competitive action or commitment will likely lead to a more aggreive repone, and vice vera. (Sengul et al (22. Thi implie that dicount are generally accepted a trategic complement. Thi paper invetigate whether thi conventional widom hold good in the context of dicount o ered to conumer who purchae bundle in which each component good i old by a di erent and independent rm. Bundled dicount have recently become very common: example range from dicount in the electricity bill in the form of voucher one can redeem at upermarket chain, o ering of cinema or amuement park ticket at ga tation or fat food chain, retaurant dicount for guet at a given hotel, car-rental dicount for paenger of a given airline, and dicount for drug cocktail made up of component produced by di erent rm, to name jut a few. Bundled dicount by independent producer were tudied by Gan and King (26 and Brito and Vaconcelo (24, under horizontal and vertical di erentiation, repectively. Thee dicount have everal implication: (i if et in advance, dicount may work a commitment device; (ii at the time they are et, the relevant objective function (joint pro t i di erent from the one that i relevant for price etting in the enuing tage (individual pro t; and (iii the dicount i typically nanced by more than one rm. Contrary to common widom, we nd that bundled dicount may be trategic ubtitute rather than complement: under ome circumtance, the bet-repone to an increae in the rival dicount may be for a pair of rm to reduce it own dicount. Thi poibility reult i illutrated within a theoretical framework baed on a impli ed verion of Brito and Vaconcelo (24. Section 2 provide a brief decription of the model. Section 3 preent the reult. Finally, Section 4 conclude. ll expreion are preented in the appendix. The trategic complement/trategic ubtitute ditinction wa introduced in the literature by Bulow et al (985. 2

3 2 The model We conider a two-product verion of Gabzewicz and Thie (979, where each product i old both by a high and alo by a low quality rm. Let X and Y be the high quality eller of product X and Y, repectively, and let B X and B Y denote the correponding low quality producer. In addition, let P j and p j denote the headline price et by j and B j, repectively, with j X; Y. We aume that rm X i allied with Y and that rm B X i allied with B Y, meaning that a pair of allied rm o ering product of imilar quality level will o er a dicount to thoe conumer who purchae both product from them. Given that there i ymmetry between allied rm, we aume that they will equally nance the dicount. 2 The dicount o ered by the high (rep. low quality producer i denoted by (rep. B. The timing of the game i a follow. t a rt tage, the pair of allied rm decide imultaneouly upon the dicount that maximize their joint pro t. fterward, the four rm et their headline price imultaneouly o a to maximize individual pro t. 3 Conumer are aumed to alway purchae one unit of each product. Moreover, conumer are uniformly ditributed on a unit quare where each axi meaure conumer valuation for quality of each product. conumer with valuation for quality X ; Y on [; ] 2 purchae from X and Y if and only if: Y > P Y p Y X > P X p X Y + X > P X + P Y (p X + p Y B where repreent the di erence between the high and the low quality verion of each product, which i aumed to be equal. The rt and econd inequalitie enure that, given that the conumer elect the high quality verion of one of the product, it will alo prefer the high quality verion of the other product, becaue the valuation for the increment in quality more than compenate for any increae in price. The third inequality, on the other hand, enure that the high quality pair of product generate more urplu than the low quality pair. The demand for each of the four poible combination of product i given by the number of conumer that verify the three relevant inequalitie. We write Q B to denote the number 2 We conider bundling by rm with the ame quality to be the natural cenario. high quality producer would probably not be intereted in being allied with a low quality one a thi would likely a ect it reputation. Further, conidering only thi cenario alo allow u to avoid having to determine the optimal way of haring the dicount in an aymmetric alliance involving a high quality and a low quality producer. 3 For a juti cation of thi timing, ee Gan and King (26 or Brito and Vaconcelo (24. 3

4 of conumer that purchae product X from rm and product Y from rm B, and likewie for the three remaining poible combination. 4 Dicount are aumed to be mall. We de ne a mall dicount a a dicount uch that the four poible combination of product have a poitive market hare for all dicount level of the competitor (if any, at the equilibrium price. Formally, we aume that ( ; B 2 [; ] 2, where i preented in the appendix. 5 To ome extent, mall dicount can be juti ed by the management literature that ha highlighted the ine ectivene of high dicount. Raghubir (998 and (24, Barat and Pawan (25 or Wu et al. (2 point out the poibility that a high dicount may trigger negative conumer deduction about the headline price or quality, or even create negative emotion due to the implicit price dicrimination involving coupon. Moreover, mall dicount are empirically more relevant, a mot oberved dicount would mot probably fall within our de nition of mall dicount. 6 The equilibrium i obtained by working backward. For a given pair of dicount, the (individual pro t maximizing price are obtained. Then, dicount which maximize joint pro t are characterized. 3 Reult Figure preent the bet-repone function for the pair of low quality rm. We can only characterize thi function numerically and it ha a downward lope: dicount are trategic ubtitute. 7 To undertand why the low quality rm may prefer to lower their dicount when rival increae their, one need to undertand how the dicount impact the allied rm joint pro t and how thi impact change with the rival dicount level. Uing i : i, joint pro t for the low quality rm i B p Y (Q BB + Q B + p X (Q BB + Q B B Q BB : Due to the fact that the equilibrium price of both product of imilar quality are ymmetric, B may be written a B 2p X (Q BB + Q B B Q BB : 4 The appendix preent the demand function in detail. 5 Thi i a common aumption in the literature. See ydemir (29 or Gan and King (26. 6 In our etting, the upper bound on the dicount level,, repreent 6% and 2% of the headline price of the high and low quality component product of the bundle (in the no-dicounting benchmark cae, repectively. 7 It can be howed that the derivative of the high quality pair of rm joint pro t with repect to it dicount i poitive, meaning that the optimal dicount for thi pair of rm i the larget admiible one. 4

5 Figure : Low quality pair of rm bet repone function The rt-order condition in B i (Q BB + Q BB (Q BB + Q B + p X Q BB + : ( B Notice that all derivative in ( are poitive: the headline price, the number of unit entitled to the dicount and the low quality rm aggregate ale increae in B. Price p X increae with B for two reaon: (i a higher dicount o ered by the low quality producer increae the demand for each low quality product; and (ii the introduction of the dicount can be interpreted a a unit cot, partially incurred by each rm, for the unit entitled to the dicount. Further, depite the fact that p X increae with the dicount, the net bundle price decreae with it, leading to a higher demand for the bundle and alo for all low quality product. The left-hand ide in ( i the dicount marginal bene t. the headline price will increae X >, the margin per unit i higher, excluding the dicount cot. Total ale will alo increae BB+Q B >. Hence, the dicount marginal bene t come from both an increae in price and in ale. The right-hand ide in ( i the dicount marginal cot. It alo include two e ect: (i all unit that were previouly old a a bundle (Q BB now entitle the correponding conumer to a higher dicount; and (ii there will be an increae in the ale entitled to the dicount BB >. The optimal dicount i obtained when the marginal revenue equal marginal cot. Now, to undertand how allied rm hould react to di erent rival dicount we need to etablih how 8 Note that changing the dicount will a ect price and quantitie in the enuing tage. 5

6 marginal bene t and cot change with. Di erentiating ( with repect to we 2 p X 2 (Q BB + Q B BB + Q 2 (Q BB + Q B + p X (Q BB Q BB Conider rt the impact of the rival dicount on marginal bene t. The headline price increae more with own dicount in the preence of the rival dicount, but thi increae impact a maller number of original unit demanded. dditionally, although the number of additional unit demanded i now higher, thee may be old at a lower or higher price than in the abence of a rival dicount. Depite the fact that the net reult i potentially ambiguou, the poitive e ect dominate, implying that there i an incentive to increae own dicount when rival increae their. for the marginal cot, when rival increae the dicount Q BB become larger. However, fewer additional unit will be old by the low quality pair of rm a a reult of a higher dicount. lthough the net e ect i again potentially ambiguou, the aggregate e ect i poitive. The following table ummarize thee e ect and alo highlight how they change with. Marginal Bene t Marginal Cot Term: t 2nd t X (Q BB + Q B p BB +Q B Q BB B Sign of derivative wrt > <? > > < {z } {z } {z } > > > Hence, if dicount are trategic ubtitute, it mut be that the increae in marginal cot dominate the increae in marginal bene t. Perhap counter-intuitively, when the high quality rival increae their dicount, the ale of the low quality bundle increae: increaing the high quality bundle dicount, increae the high quality headline price, leading ome conumer who were purchaing product of di erent qualitie to witch to the low quality bundle. Thi then make it more expenive to increae the low quality bundle dicount, a the number of conumer entitled to it become larger. 9 9 Notice that the impact of the dicount on headline price would not exit if dicount and price were et imultaneouly, a one would expect to be the cae if dicount were intead o ered by a multi-product rm. 6

7 4 Concluion Bundled dicount play an increaingly important role a a trategic tool. In many intance, the dicount are given by pair of independent rm who agree to cut price charged to conumer who purchae from both of them. Given that price of rm competing for the ame conumer are trategic complement, one would expect thee dicount to be trategic complement a well. However, in ome circumtance, they may be trategic ubtitute. In thi paper, we analyze the cae of competition between independent vertically di erentiated producer o ering bundled dicount. We nd that the low quality pair of producer may prefer to lower their dicount after an increae in the dicount o ered by the high quality producer. The reaon i that the demand for their bundle may actually increae with the rival dicount, making their own dicount very expenive. the high quality dicount increae, o will the correponding headline price. Thi mean that conumer who were previouly purchaing product of di erent quality may prefer to witch to the low quality bundle and bene t from the aociated dicount. In repone, thi may lead the latter pair of producer to prefer to decreae their dicount. Reference [] ydemir, R., (29, Eay on Bundling and Low Cot ir Carrier Pricing, Ph.D. Diertation, The Univerity of Texa at utin, vailable for download at: [2] Barat, S. and. K. Pawan, (25 "Do higher face-value coupon cot more than they are worth in increaed ale?", Journal of Product & Brand Management, Vol. 4 (6, pp [3] Brito, D. and H. Vaconcelo (forthcoming, Inter- rm Bundling and Vertical Product Di erentiation Scandinavian Journal of Economic. [4] J. Bulow, J. Geanakoplo, and P. Klemperer (985, Multimarket oligopoly: trategic ubtitute and trategic complement. Journal of Political Economy 93, 488-5, [5] Gabzewicz, J. and Thie, J.-F. (979, Price Competition, Quality and Income Diparitie, Journal of Economic Theory 2, [6] Gan, J. and King, S. (26, Paying for Loyalty: Product Bundling in Oligopoly, Journal of Indutrial Economic, 54(,

8 [7] Raghubir, P. (998 "Coupon Value: a Signal for Price?", Journal of Marketing Reearch, Vol. 35 (3, pp [8] Raghubir, P. (24 "Coupon in context: dicounting price or decreaing pro t?", Journal of Retailing, Vol. 8, pp. 2. [9] Sengul, M., J. Gimeno and J. Dial (22, Strategic Delegation : Review, Theoretical Integration, and Reearch genda, Journal of Management, 38(, [] Wu, C.-C, Yi-Fen Liu, Ying-Ju Chen, Chih-Jen Wang, (2 "Conumer repone to price dicrimination: Dicriminating bae, inequality tatu, and information dicloure timing in uence", Journal of Buine Reearch, available online ppendix Demand Function With no dicount, conumer purchae product i X; Y from rm i if and only if where V i the reervation price. V + i P i > V + i B p i, i > i : P i p i ume the high quality rm introduce dicount : Then, a conumer characterized by: p X X > X P X and Y > Y P Y p Y will till purchae from X ; Y : p X X > X P X and Y < Y P Y p Y will purchae X ; Y if X P X + Y P Y + > X P X + Y B p Y, Y > a Y : P Y p Y : p X X < X P X and Y < Y P Y p Y will purchae X ; Y if X P X + Y P Y + > X B p X + Y B p Y, X > P X p X + P Y p Y Y : p X X < X P X and Y > Y P Y p Y will purchae X ; Y if X P X + Y P Y + > X B p X + Y P Y, X > a X P X p X : ume additionally that the low quality rm introduce dicount B : Then, a conumer characterized by: 8

9 X < a X and Y > Y will purchae B X ; B Y if X B p X + Y B p Y + B > X B p X + Y P Y, Y < b Y : P Y p Y + B : X > X and Y < a Y will purchae B X ; B Y if X B p X + Y B p Y + B > X P X + Y B p Y, X < b X : P X p X + B : X > a X and Y > a Y and X > P X p X +P Y p Y Y will purchae B X ; B Y if X B p X + Y B p Y + B > X P X + Y P Y +, X < P X p X + P Y p Y + B Y a X + b Y Y : Demand function, reulting from the relevant area in the ( X ; Y pace, are: P X p X + Q X ;B Y B PY p Y ; P Y p Y + Q BX ; Y B PX p X ; P Y p Y Q X ; Y P X p X ( + B 2 ; 2 2 PY p Y + Q BX ;B Y B PX p X + B ( + B 2 : 2 2 The pro t function at the pricing tage are: X P X (Q X B Y + Q X Y Y P Y (Q X Y + Q BX Y X p X (Q BX B Y + Q BX Y Y p Y (Q BX B Y + Q X B Y 2 (Q X Y 2 (Q X Y B 2 (Q B X B Y B 2 (Q B X B Y Uing i : i and olving the ytem of rt-order-condition one obtain: P X B B + 5 B B B (5 + 5 B + 6 P Y B B + 5 B B B (5 + 5 B + 6 p X B B + 3 B + 5 B B B (5 + 5 B + 6 p Y B B + 3 B + 5 B B B (5 + 5 B + 6 9

10 and Q X ;B Y B + 5 B B B B 2 (5 + 5 B ; Q BX ; Y B + 5 B B B B 2 Q X ; Y Q BX ;B Y (5 + 5 B B + 28 B B B 8 2 B 2 2 B 4 3 B 6 3 B B (5 + 5 B B + 88 B B B 7 4 B 2 2 B 8 2 B 6 3 B 4 3 B B (5 + 5 B : For all egment of demand to be poitive, one need to aume that: 4 5 B B B (2 2 5 B 3 2 B 2 2 (3 where (3 implie (2. uming that both dicount cannot exceed, it follow that (3 hold for any dicount if and only if Hence, we aume throughout the paper that ( ; B 2 [; ], with 2 5.

11 Comparative Static The derivative referred in Section 3 (Q BX ;B Y + Q X ;B Y 6 B 5 B B B + 2 B (5 + 5 B (Q BX ;B Y + Q X ;B Y 5 6 B B 5 3 B 2 B 5 2 B + 2 (5 + 5 B (Q BX ;B Y + Q X BX ;B BX B + 8 B B B B B + 4 (5 + 5 B > B 8 B B B 85 4 B 63 2 B B 32 3 C B 28 3 B B + 4 (5 + 5 B > B 78 B B B 65 4 B B 36 2 B 23 3 B 7 3 C B B + 8 (5 + 5 B > B 5572 B Q BX ;B B B B B B 3 3 B 3 3 B B 456 (5 + 5 B < X B + 8 B B B B B + 2 (5 + 5 B X B + 8 B B + 3 B B B (5 + 5 B X B + 48 B B B B B 2 (5 + 5 B B + 43 B B B B B (5 + 5 B > The ign of ome derivative were etablihed numerically, under the aumption of mall dicount.

12 2 p X (Q BB + Q B BB + (Q BB + Q 2 (Q BB + Q B Q > t the dicount tage, the objective function i B X + Y p X (Q BX B Y + Q BX Y + p Y (Q BX B Y + Q X B Y B (Q BX B Y The rt-order-condition are: 2 6 B 5 B ( B B B B (5 + 5 B + 6 Figure preent thi function. C 2