Add-on Policies under Vertical Differentiation: Why Do Luxury Hotels Charge for Internet Whereas Economy Hotels Do Not?

Transcription

1 Add-on Poicies under Vertica Differentiation: Wy Do Luxury Hotes Carge for Internet Wereas Economy Hotes Do Not? Song Lin Hong Kong University of Science and Tecnoogy June 2015 Abstract Tis paper examines firms product poicies wen tey se an add-on (Internet service) to a base good (ote rooms) under vertica differentiation (four- vs. tree-star otes). Teoretica anaysis uncovers te differentia roes of add-ons for verticay differentiated firms. A firm wit iger base quaity aways ses an add-on as optiona so tat iger-taste consumers sef-seect to buy it. Tis incentive to price discriminate appies to a ower-quaity firm wo, owever, as to ower te add-on price to ure consumers considering te iger-quaity base good witout te add-on. If providing te add-on is not costy, te ower-quaity firm may se it as standard. Tis equiibrium potentiay expains te puzze tat ower-end otes are more ikey tan iger-end ones to offer free Internet service. Empirica examination of a sampe of otes tat are ikey to be in a monopoy or vertica duopoy market provides suggestive evidence for tis prediction. Surprisingy, an optiona add-on can intensify competition, in contrast to standard concusions in te iterature. If bot firms se an optiona add-on, tey wi price aggressivey to compete for consumers wo trade off te iger-quaity base versus te ower-quaity base good pus te add-on. Atoug seing te add-on as optiona is uniateray optima, equiibrium profits may reduce - a Prisoner s Diemma outcome.

2 1 Introduction Atoug Internet service is a necessity and is avaiabe in most otes, ony 54% of uxury otes provide it for free. In contrast, te percentage grows to 72%, 81%, 93%, and 91% for upscae, mid-priced, economy, and budget otes, respectivey. 1 Tis penomenon appears to be counter-intuitive, attracting considerabe pubic attention and media coverage. 2 Wy does te penomenon persist? Te answer to te question may ave important manageria impications. In many industries, it is common for firms to se a base good or service as teir primary business, and ten se a compementary item or upgrade (ereafter, add-on ). 3 Exampes incude airines seing drinks and snacks on a figt, car manufacturers seing upgrades suc as GPS and eater seats on top of a base mode, and mobie appications offering in-app purcases or premium upgrades. Soving te puzze eucidates wat product poicies firms soud adopt: Soud tey se an add-on separatey from te base good as optiona, se it as standard (i.e., free), or not se it at a? Existing pricing teories do not offer adequate expanations to tis puzze. Conventiona wisdom from monopoy pricing suggests tat seing an add-on as optiona aows a firm wit market power to price discriminate to enance profit. Tis argument, owever, contradicts te practice of ower-end otes. A simpe expanation woud be tat consumers staying at iger-end otes are ess price-sensitive. 4 However, tis argument woud suggest tat 1 Te penomenon aso appies to oter ote amenities suc as breakfast and oca pone cas. Te data source is 2012 Lodging Survey by American Hote & Lodging Association. In te empirica section I provide detais of te survey data. 2 To name a few: Te price of staying connected (New York Times, 5/6/2009), Hote guests crave free Wi-Fi (Los Angees Times, 9/6/2010), Luxury otes free up Wi-Fi (Wa Street Journa, 5/5/2011), Wi-Fi in otes: te most unkindest carge of a (Te Economist, 5/16/2011), Some otes wit free Wi-Fi consider carging for it (USA Today, 6/22/2012), Wi-Fi fees drag ote satisfaction down (CNN, 7/25/2012). 3 Some add-ons are better described as surcarges, wic are mandatory or necessary after te purcase of a base good. Exampes incude taxes for most services and goods, fue surcarges for airines, concession recovery fees for car renta at airport ocations, etc. A recent stream of beaviora researc on partitioned pricing expores ow consumers react under tis situation (e.g., Morwitz et a. 1998, Ceema 2008). Tis paper restricts attention to add-ons tat are not mandatory or not necessary on te purcase of a base good. 4 Tere are severa reated expanations aong te same ine. For exampe, one may argue tat consumers 1

3 te iger-end otes carge a iger tota price rater tan separate Internet carges from room rates. Sugan and Kumar (2014) compare te ote industry to te airine industry and argue tat it is optima for a monopoist wit a product ine of base services to bunde add-ons wit its ower-end base to decrease te base differentiation wen te differentiation is arge (ote industry), and to unbunde add-ons wit its ower-end base wen te base differentiation is sma (airine industry). However, tis teory does not expain wy te penomenon persists even wen iger-end and ower-end otes are not owned by te same company, and wy poicies are different for different types of add-ons witin an industry (e.g., mini-bar, aundry, or airport sutte services in te ote industry). I propose a different but compementary expanation tat vertica differentiation between competing firms pays a roe. I deveop a competitive teory of add-on pricing to examine ow vertica differentiation can ead to a divergence in product poicy. Te teory eads to tree interesting insigts. First, te teory identifies te differentia roes of add-ons for verticay differentiated firms. A firm wit iger base quaity beaves more or ess ike a monopoist. Seing an add-on as optiona at a ig price serves as a screening or segmentation device so consumers wit iger tastes for quaity sef-seect to buy te expensive add-on. Tis incentive to screen consumers aso appies to a firm wit ower base quaity. However, te ower-quaity firm is incentivized to ower te add-on price to ure tose consumers, wo may consider buying te iger-quaity base witout paying for te add-on, to switc to te ower-quaity base wit te add-on. Tis vertica differentiation roe of te add-on is absent from extant iterature on add-on pricing, wic focuses on unobserved add-on prices wit orizonta or no differentiation (La and Matutes 1994, Verboven 1999, Eison 2005, Gabaix and Laibson 2006). 5 Due to te trade-off between screening and differentiation, te ower-quaity firm s at iger-end otes ave corporate accounts covering teir expenses wereas consumers at ower-end otes trave wit teir own accounts. Anoter reated argument is tat iger-end otes customers are typicay business traveers wereas ower-end otes ave more eisure traveers. 5 Te term add-on pricing as been used to refer to a specific situation wit unobserved add-on prices (Eison 2005). In tis paper te term refers to broader probems tat invove pricing of a base good and an 2

4 poicy is sensitive to te efficiency of suppying te add-on. Te firm wi not se te add-on if it is too costy to provide te add-on to improve quaity because it as to carge a ig add-on price tat discourages consumers from buying (e.g., mini-bar). In equiibrium, te ower-quaity firm se te add-on ony if it is not too costy. If te cost becomes sufficienty sma (e.g., Internet service), te add-on price wi be so ow tat a consumers wo buy te base from te ower-quaity firm wi aso pay for te add-on. Consequenty, te igerquaity firm wi se te add-on as optiona, wereas te ower-quaity firm wi se it as standard. Tis equiibrium outcome provides one possibe expanation of te styized fact. Examining a sampe of monopoy and duopoy markets wit vertica differentiation in te American ote industry, I find suggestive evidence for te teoretica predictions wen te cost of an add-on is very sma (i.e., Internet service). On te one and, a ote at te iger end of a vertica duopoy market is as ikey as a monopoy ote to carge for Internet service, consistent wit te teory tat iger-quaity firms focus on screening consumers, beaving ike a monopoist. On te oter and, a ote is more ikey to offer free Internet service if it is at te ower end of a vertica duopoy market. Tis finding supports te teory tat vertica differentiation introduces a trade-off for ower-quaity firms, wic find it optima to se an add-on as standard rater tan se it as optiona. Concusions are robust even after controing for a number of potentiay confounding factors suc as ote segment, ocation, size, age, operation, etc. Second, te teory eads to a surprising prediction tat seing an add-on as optiona intensifies competition. Since a iger-quaity firm ses an add-on to its iger-taste consumers, eaving some ower-taste consumers wo do not buy te add-on, it creates an opportunity for a ower-quaity firm to ower its add-on price to induce switcing. Te firms ten price aggressivey to compete for tese margina consumers wo trade off te iger-quaity base good versus te ower-quaity base good incuding te add-on. Atoug te optionaadd-on, regardess of te observabiity of te add-on price. 3

5 add-on poicy is uniateray optima, a Prisoner s Diemma emerges in wic bot firms ose profits in equiibrium. Te resut is striking. Extant iterature predicts tat seing an add-on as optiona eiter as no impact on firm profits under competition (La and Matutes 1994), or softens price competition (Eison 2005). Te profit-irreevant resut is based on te argument tat any profit earned from seing a ig-priced add-on is competed away on te base price. Te competition-softening resut inges on te idea tat wit te add-on prices unobserved naturay, firms create an adverse seection probem tat makes price-cutting unappeaing, tereby raising equiibrium profits. In contrast, I identify a mecanism by wic seing an add-on urts firm profits. Te mecanism does not rey on te unobservabiity of add-on prices. It is te interaction between te screening effect and te differentiation effect tat reverses standard concusions on te profitabiity of seing an add-on. Due to te intensified competition, te iger-quaity firm may want to commit to a standard-add-on poicy, and te ower-quaity firm to commit to a no-add-on poicy, if suc commitments are possibe. Luxury cars, for exampe, are more ikey tan economy cars to offer some advanced features suc as standard eater seats, GPS navigation, side airbags, etc. Tird, wen consumers do not observe add-on prices, od-up probems arise naturay. However, unike oter settings in te iterature, vertica differentiation moderates te effects of od-up on firm profits in tis context. Te iger-quaity firm s poicy is unaffected by te unobservabiity of te add-on price, because its consumers aready expect te add-on to be expensive due to te firm s screening incentive. Te od-up effect coincides wit te screening effect for te iger-quaity firm. Anticipating being ed up by te ower-quaity firm, some consumers refrain from buying from it and switc to te iger-quaity base good witout paying for te add-on. Consequenty, te iger-quaity firm demands a iger base price, but te ower-quaity firm is forced to ower its base price wie keeping te add-on price ig. In equiibrium te iger-quaity firm is better off, wereas te ower-quaity firm is worse off, suggesting tat te iger-quaity firm as no incentive to advertise te add-on 4

6 price, wereas te ower-quaity firm as a strict incentive to advertise. Tis prediction contrasts sarpy wit extant resuts tat a od-up probem as no impact on firm profits under competition because profits earned by oding up consumers ex post are competed away by owering base prices (i.e., oss eader ; La and Matutes 1994). Reated Literature Tis study reates to broader iterature on price discrimination and muti-product pricing. Not surprisingy, add-on pricing can be a form of second-degree price discrimination. A base good incuding an add-on versus te base good aone can be viewed as two quaity eves. If firms se an add-on as standard, tey essentiay se te same quaity to a consumers wit no price discrimination. If firms instead adopt an optiona-add-on poicy, tey se te bunde (i.e., te iger-quaity eve) to consumers wit iger tastes for quaity wie seing ony te base (i.e., te ower-quaity eve) to ower-taste consumers. In monopoy markets, it is generay optima for firms to price discriminate. Te probem is muc arder to anayze under imperfect competition. Extant studies of competitive second-degree price discrimination (Stoe 1995, Armstrong and Vickers 2001, Rocet and Stoe 2002, Eison 2005, Scmidt-Mor and Vias-Boas 2008) examine settings in wic firms are symmetric, finding tat firms engage in price discrimination if sufficient consumer eterogeneity exists. Tey do not consider te possibiity of vertica pressure competing firms face, a scenario tat arises often in te rea word. One exception is Campsaur and Rocet (1989), wo study differentiated firms in a duopoy market competing by offering ranges of quaity to eterogeneous consumers. After firms investments in quaity ranges, tey determine te optima noninear pricing poicies. Te price-setting game, given differentia quaity ranges, is simiar in spirit to te pricing game I study ere. However, unike tose autors, I study te context of add-on pricing in wic quaity is discrete, and derive impications of competitive price discrimination on profitabiity. 5

7 Te resut tat seing an add-on intensifies competition aso reates to severa findings in te iterature. Atoug it is generay true tat monopoists find it optima to price discriminate among consumers, tis concusion is no onger robust under competitive settings. Price discrimination can intensify competition, tereby urting profits. One mecanism by wic tis resut arises is competitive tird-degree price discrimination (Tisse and Vives 1988, Saffer and Zang 1995, Corts 1998). Corts (1998) points out tat wen firms ave a divergent view on te ranking of consumer segments (i.e., a strong market for one firm is weak for te oter), it is possibe tat price discrimination eads to ower prices in a market segments, reducing profits. 6 Anoter mecanism giving rise to tis resut is competitive mixed bunding in te two-stop sopping framework (Matutes and Regibeau 1992, Anderson and Lerut 1993, Armstrong and Vickers 2010). 7 Practicing mixed bunding migt trigger fierce price competition, owering prices for component products. Consequenty, profits reduce. Tis paper identifies an aternative mecanism tat differs substantiay in terms of modeing framework and business context. Te add-on pricing probem studied ere differs from tird-degree price discrimination because firms do not know consumers preferences, and tus rey on incentive compatibiities to practice price discrimination. Te probem is aso different from muti-product bunding because an add-on is ony avaiabe and vauabe conditiona on te purcase of a base good. 8 Neverteess, te recurring teme underying te competition-intensifying resut appears to be tat competing firms price aggressivey to acquire consumers wo trade off between buying a iger-quaity eve from one firm versus buying a ower-quaity eve from anoter. Finay, tis paper reates to growing academic and industria interest in drip pricing. 9 6 Many cases exist in wic tis condition does not od, and tus competing firms are better off in equiibrium (e.g., Cen et a. 2001, Saffer and Zang 2002). 7 Wen competing firms offer mutipe products, tey can eiter se te component products aone (i.e., component pricing), or se te products in a bunde (i.e., pure bunding), or bot (i.e., mixed bunding). 8 Consumers cannot buy te add-on witout buying te base good, but tey can buy te base good aone witout buying te add-on. For exampe, a consumer cannot access Internet service in a ote if se does not stay at te ote, but se can stay in te ote room witout using te Internet service. 9 Te Federa Trade Commission defines drip pricing as a pricing tecnique in wic firms advertise ony 6

8 Te eading teory tat expains wy firms adopt drip pricing is tat it is profitabe to expoit myopic consumers wo do not anticipate te idden cost. Gabaix and Laibson (2006) sow tat firms may coose not to advertise add-on prices (i.e., srouding) even under perfect competition. Suman and Geng (2012) extend te mecanism to te situation in wic firms are ex ante different in bot orizonta and vertica dimensions. Daremöer (2013) introduces a commitment decision of srouding or unsrouding, wic can ater underying incentives to unsroud. Muir et a. (2014) provide empirica evidence of drip pricing tat driving scoos take advantage of te fact tat many students are not aware of extra driving scoo fees wen tey take a base course of driving instruction. Unike tese autors, I examine ong-run market outcomes in wic consumers know or correcty anticipate add-on prices in equiibrium. Tis assumption is not unreasonabe, given tat consumers migt earn about prices troug repeat purcases and/or word-of-mout, 10 and in many cases, firms advertise add-on poicies because tey care about reputation or reguations require discosure. It is unikey tat te motivating styized fact is driven by consumer myopia, given tat repeat purcases are common in te ote industry and Internet service is a igy expected and frequenty used feature. 11 Resuts from tis study suggest tat vertica differentiation not ony as profound impacts on add-on poicies even under compete price information, but aso interacts wit firms incentives to advertise add-on prices wen tey are unobservabe. part of a product s price and revea oter carges ater as te customer goes troug te buying process. Te additiona carges can be mandatory carges, suc as ote resort fees, or fees for optiona upgrades and add-ons. 10 For exampe, aving stayed at Marriott and earned tat Internet service costs $13, a consumer may keep tis in mind te next time se books a room at te same ote or at anoter ocation of te same cain. 11 If consumers are boundedy rationa, ten Internet fees soud be srouded and iger tan margina costs at bot te uxury and economy otes. 7

9 2 A Teory of Add-on Poicy under Vertica Differentiation In tis section, I present a teory tat expains wy and wen a divergence in product poicy arises as an equiibrium outcome. I first write down te simpest mode tat iustrates te key underying mecanism, and ten reax some of te simpifying assumptions to demonstrate tat tey do not ater te main message of te mecanism. 2.1 Mode Setup Tere are two firms j {, }, tat differ in terms of te quaity of te base good V suc tat V > V > 0. Te quaity difference, or quaity premium, is V. Te margina cost of te base good is normaized to zero for bot firms. In an extension discussed ater, I aow te margina cost to be different for te two firms. In addition to te base good, an add-on tecnoogy is avaiabe. Te add-on as vaue w and costs c, te same for bot firms. Again, te symmetric assumption is made ony to simpify anaysis. Quaitative concusions remain argey unaffected in an extension wit asymmetric add-on considered ater. Te efficiency of suppying te add-on is measured by te cost-to-vaue ratio, α = c/w, wic pays an important roe in te equiibrium anaysis. It is assumed tat te quaity premium is greater tan te vaue of te add-on, V > w, aowing interesting equiibria to arise. Eac firm can set base price P j and add-on price p j. A continuum of consumers differ in teir margina vauation, or taste, for quaity. Te taste parameter, θ, is distributed uniformy wit θ [θ, θ] and θ > Two assumptions are made trougout te anaysis. First, θ > 2θ, so tere is a sufficient amount of consumer eterogeneity in te market. Second, θ > α, so tere are positive saes of te add-on in 12 Te assumption tat te ower bound is positive, combined wit a sufficienty arge base quaity V j, ensures tat te market is fuy covered. It simpifies anaysis by focusing on te interaction between te two firms, assuming away te outside option of not buying from any firm. 8

10 equiibrium. Te utiity of buying from firm j for type-θ consumer is θv j P j U θj = θ(v j + w) P j p j if ony te base good is purcased; if bot te base good and te add-on are purcased. (1) Te base and add-on vaues V and w are bot common knowedge to a parties. Tis is not an unreasonabe assumption for industries suc as te ote industry in wic consumers possess sufficient knowedge or information due to say repeat purcases. 13 However, consumers know teir own tastes θ, but te firms do not. Te firms ony know te distribution of tastes, and ence rey on incentive compatibiities to screen consumers or price discriminate. It is wort noting tat te assumption tat te unobserved consumer preferences are summarized entirey in one dimension, θ, may appear strong, but it keeps te mode tractabe. An aternative interpretation is tat tastes are te inverse of price sensitivities. 14 Te impicit restriction beind tis setup is tat wiingness-to-pay for te base good and for te addon (θv j and θw) correate perfecty. Neverteess, te mecanism does not rey on tis assumption, as sown in an extension wit imperfecty correated tastes in te Appendix. Wat is necessary is tat tere is unobserved eterogeneity in bot te base good and addon, enabing consumers to trade off between te add-on and te base quaity. 15 For price discrimination to arise, te singe-crossing property is necessary suc tat iger tastes for te vaue of an add-on and for a base quaity impy iger wiingness-to-pay for te add-on 13 Tere are, of course, situations in wic consumers experience uncertainty about V and/or w. If firms ave superior knowedge on tese vaues, ten te add-on can signa te base quaity. For exampe, Bertini et a. (2009) sow tat add-on features can infuence consumers evauations of a base good about wic tey are uncertain. How firms design product poicies under tis situation is an interesting direction to expore, but it is beyond te scope of tis paper. If firms are aso uncertain about tese vaues, insigts from tis simper specification of consumer utiity may appy. 14 One can specify an equivaent preference mode suc tat te utiity of buying bot a base and an add-on is given by U θj = V j + w (P j + p j )/θ. 15 Tis feature distinguises te paper from Dogan et a. (2010). In teir mode of competitive seconddegree price discrimination wit vertica differentiation in te context of rebates, tere is no unobserved eterogeneity in tastes for te base quaity. 9

11 and for te iger-quaity base. Te strategic interaction is modeed as a fu-information simutaneous-move game. Bot firms announce prices simutaneousy, (P, p ) and (P, p ). Consumers observe a prices and decide wic firm to visit and weter to pay for an add-on from te cosen firm. Te formuation naturay buids on two styized modes. If tere is no add-on, te mode reduces to a duopoy mode of vertica differentiation (Saked and Sutton 1983). If tere is no competition, te mode reduces to a monopoy mode of noninear pricing (Mussa and Rosen 1978) wit continuous-type consumers and discrete quaities. Eac reduced mode is straigtforward to sove. However, combining te two features compicates equiibrium anaysis dramaticay due to te many possibiities of market outcome. Specificay, eac firm can price its base and add-on to impement any of te foowing tree outcomes, taking into account consumers incentive compatibe decisions: No Add-on: No consumer buys te add-on. A consumers buy just te base good. Standard Add-on: A consumers buy te add-on. It is essentiay bunded wit te base good because ony te tota or bunde price matters. Optiona Add-on: Some but not a consumers buy te add-on. Te iger-type consumers buy it, wereas te ower-type consumers buy ony te base. Tere are nine possibe market configurations, depending on te impementations by bot firms. Eac configuration constitutes a possibe equiibrium profie. To prove te existence of an equiibrium for eac profie, one as to examine, for eac firm, a non-oca deviations tat ead to any form of te remaining eigt possibe market configurations. However, te soution to te game can be simpified by observing tat te iger-quaity firm aways serves te igest-type consumers and tus may ave a strong incentive to se te add-on as optiona in equiibrium. Te next sub-section formaizes tis intuition. 10

12 2.2 Te Higer-quaity Firm Focuses on Screening If te iger-quaity firm impements te optiona-add-on poicy, it essentiay divides its poo of consumers into two segments. Te iger-type consumers, θ [ˆθ, θ], buy bot te base and te add-on. Type ˆθ is te intra-margina consumer wo is indifferent between buying te bunde and buying ony te base, and it is equa to p /w. Te remaining ower-type consumers, θ [ˆθ, ˆθ ], buy te base ony. Tis segmentation is a resut of te singe-crossing property tat iger-type consumers sef-seect to buy te add-on. Type ˆθ is te margina consumer wo is indifferent between buying from te iger-quaity or ower-quaity firm. Tis margina consumer is ony affected by base price P, and te add-on price is irreevant. Te firm s profit decomposes into two additive profit components Π = (θ ˆθ )P + (θ ˆθ )(p c). (2) }{{} π (p ) Te first is te profit from seing te base good, independent from te add-on price since it is irreevant to te margina consumer ˆθ. Te second is te additiona profit from seing te add-on, independent from te base price. Witout considering incentive constraint ˆθ ˆθ, to maximize profit, te iger-quaity firm simpy cooses te appropriate base and add-on prices to maximize te two components separatey. If, owever, te incentive constraint is binding, a consumers wi buy te bunde. In tis case, te firm is seing te add-on as standard and a singe bunde price P + suffices. Since te firm serves consumers wit te igest tastes in te market, it reaxes te pressure for a binding constraint. Just as in a monopoy market, te iger-quaity firm can easiy find te optiona-add-on poicy stricty better tan te standard-add-on poicy. Te foowing emma formaizes tis observation. (A proofs are provided in te Onine Appendix.) Lemma 1. For te iger-quaity firm, seing te add-on as standard is stricty dominated 11

13 by seing te add-on as optiona, if: 1. P > α V wen te ower-quaity firm does not se te add-on, or 2. P + > α( V w) wen te ower-quaity firm ses te add-on. Te intuition beind tis emma is simpe. Wen te iger-quaity firm ses te addon as standard, te add-on price is set sufficienty ow so tat a of its consumers buy it. Consider a oca deviation wereby te firm increases te add-on price by a sma amount ɛ and decreases te base price by te same amount. Ten some consumers refrain from paying for te add-on (i.e., te firm impements te optiona-add-on poicy). On te one and, increasing te add-on price does not ose many consumers wo ave originay bougt te add-on, but it generates additiona revenue from tose iger-type consumers wo continue to pay for it. On te oter and, owering te base price expands te market. Acquired consumers are of te ower types so te oss due to te ower base price is quite imited. Te tota profit is ten increased. Note tat te argument requires tat tere is sufficient number of different types (more tan two) so tat a oca deviation by separating te prices is profitabe. 16 Tis intuition is te simiar to tat in a monopoy market. Despite facing competitive pressures from te ower-quaity firm, te iger-quaity firm beaves ike a monopoist. Te first main proposition foows. Proposition 1. In any equiibrium, if it exists, te iger-quaity firm ses te add-on as optiona. Te mecanism for te iger-quaity firm accords wit wat many managers ave in mind. One reason uxury otes carge for Internet service is because tey can. Seing optiona Internet service is so ucrative tat tese otes do not want to give up tis source of revenue. One driving force is te firm s incentive to screen consumers, an effective way to 16 Wit just two types of consumers, it can easiy ead to te concusion tat seing an add-on as standard is optima, as in Eison (2005) and Sugan and Kumar (2014). 12

14 boost sort-term profits. Tis incentive soud aso appy to te ower-quaity firm, given tat it aso serves a poo of consumers wit eterogeneous tastes. Wy does te ower-quaity firm beave differenty? Te next sub-section provides te answer. 2.3 Te Lower-quaity Firm Trades off Screening and Differentiation Having sown tat te ony possibe impementation of te iger-quaity firm is te optionaadd-on poicy, tere are ony tree possibe equiibrium profies to be considered, depending on te ower-quaity firm s impementation. In wat foows I deveop te equiibrium in wic te ower-quaity firm ses te add-on as optiona. Te oter two possibe equiibria become straigtforward given tis deveopment. Te ower-quaity firm now targets consumers of ower types, θ [θ, ˆθ ]. Simiar to te iger-quaity firm, it segments consumers into two groups. Te ower-type consumers, θ [θ, ˆθ ], buy ony te base good. Te intra-margina consumer, wo is indifferent between buying te bunde and buying ony te base, is given as ˆθ = p /w. Tis consumer does not react to te base price of te iger-quaity firm. Consumers of iger types, θ [ˆθ, ˆθ ], buy bot te base and add-on. Te margina consumer, wo is indifferent between te two firms, ˆθ, depends on te ower-quaity firm s tota price of te base and add-on, P + = P + p. Te profit is Π = (ˆθ θ)p + (ˆθ ˆθ )(p c). Like its riva, te ower-quaity firm is incentivized to set a ig add-on price to aow te consumers sef-seect. Tose wo ave a iger taste for quaity consider te ig-priced add-on, and te ower-type consumers consider ony te base. Unike its riva, owever, te ower-quaity firm aso uses te add-on to attract consumers wo consider ony te base from te competitor. Te firm attempts to keep its add-on price reasonaby ow to attract tese potentia switcers. To see te optima pricing strategy tat resoves tis trade-off, it 13

15 is instructive to rewrite te firm s profit as Π = (ˆθ θ)(p + c) (ˆθ θ)(p c). (3) }{{} π (p ) In tis decomposition, te first component depends ony on bunde price P +, and te second depends ony on add-on price p. Te unconstrained probem is soved by maximizing eac component separatey. Te intuition can be understood as foows. Te ower-quaity firm advertises an attractive bunde package (e.g., a 3-star ote offers Internet incuded or stay-connected packages) to its potentia consumers, θ [θ, ˆθ ], and convinces a to visit. Once consumers accept te offer, te firm excudes te owest-type consumers, θ [θ, ˆθ ], from consuming te add-on by subsidizing tem to not consume it. In tis way, te firm attracts its most vauabe consumers, θ [ˆθ, ˆθ ], wie avoiding unnecessary costs of suppying te add-on to te owest-type consumers, wo do not vaue it muc. Te strategic interaction between te two firms reduces to te competition between te ower-quaity firm s bunde and te iger-quaity firm s base good. Tey compete for te margina consumer wo is indifferent between te two, given by ˆθ = (P P + )/( V w). Te competition is te same as a duopoy mode of vertica differentiation, 17 except tat te quaity premium is V w instead of V, and tat te ower-quaity firm s price is P + instead of P. In equiibrium, te prices are P = 1 3 ( V w)(2θ θ) c, and P = ( V w)(θ 2θ) + 2 c, (4) 3 and te margina consumer is 17 See Tiroe (1988) for a styized mode. ˆθ = 1 c (θ + θ) 3 3( V w), (5) 14

16 wic determines te equiibrium market sare of eac firm. Note tat equiibrium margina consumer, ˆθ, decreases wit add-on vaue w. As te vaue grows, two opposite effects occur. On te one and, tere is a direct effect of increasing demand for te ower-quaity firm, and decreasing demand for te iger-quaity firm, because consumers obtain iger utiity from te ower-quaity firm due to te added vaue of te add-on. For fixed prices, te margina consumer moves upward as w increases. On te oter and, tere is an indirect effect stemming from strategic price responses to canges in product quaity. Te igerquaity firm owers its base price as vaue w increases. Contrariy, te ower-quaity firm raises its bunde price to expoit acquired consumers wo ave iger tastes. Te price gap is reduced, moving te margina consumer downward. In equiibrium, wic effect dominates depends on te cost of te add-on reative to te cost of te quaity premium. In te current setup, te strategic effect dominates given tat te cost of te quaity premium is sma (i.e., assumed to be zero), and ence te margina consumer becomes ower as w increases. 18 Independent of strategic interactions tat determine equiibrium market sares, te firms set an optima add-on price. Add-on prices p and p are cosen to maximize π (p ) and π (p ) in Equations (2) and (3) respectivey, wic ead to p = 1 2 (θ + α)w, and p = 1 (θ + α)w, 2 wit resuting intra-margina consumers: ˆθ = 1 2 (θ + α) and ˆθ = 1 (θ + α). Te optima 2 add-on prices refect underying consumer tastes. Atoug te add-on is te same for bot firms, te price is iger at te iger-quaity firm. Tis accords wit te casua observation tat Internet fees at iger-end otes are iger tan tose at ower-end otes (if tey carge for it). Furtermore, te add-on price at te iger-quaity firm is iger tan te margina cost, suggesting tat it is a profitabe business. However, te price is consideraby 18 In te extension in wic te margina cost of te base good is asymmetric, tis concusion ods as ong as te cost of te add-on is greater tan te cost of te quaity premium. 15

17 ower at te ower-quaity firm, even ower tan te margina cost. In fact, te ower-quaity firm prices te add-on significanty ower tan wat it woud ave carged if tere were no competition. To see tat, imagine tat te ower-quaity firm is te monopoist for a market of consumers wit types θ [θ, θ ]. Te maximization probem woud ead to an add-on price of p = 1(θ 2 + α)w, wic is greater tan p in te equiibrium under vertica differentiation because θ > θ. Tis is true even toug θ can be muc smaer tan θ. Te fact tat te ower-quaity firm serves te consumers wit ower tastes is not te main driver of te ow add-on price; vertica differentiation forces te firm to price it consideraby ow, even beow te margina cost. 2.4 Incentive Compatibiity and Equiibrium Outcomes Te preceding anaysis uncovers te equiibrium pricing under te scenario in wic bot firms se te add-on as optiona. Tis equiibrium exists as ong as te foowing incentive constraints od: (1) ˆθ > ˆθ, (2) ˆθ > ˆθ, (3) ˆθ > θ. Te first incentive constraint ods as ong as V > w. Intuitivey, tis means tat as ong as te quaity premium is greater tan te add-on vaue te ower-quaity firm provides, some consumers prefer te iger-quaity base good to te ower-quaity bunde. Te ast two constraints depend cruciay on te cost of suppying te add-on reative to its vaue, and determine weter te ower-quaity firm ses te add-on, or se it as standard or as optiona. On te one and, te margina consumer wo is indifferent between te two firms, ˆθ, decreases in margina cost of add-on c for a fixed vaue of te add-on, according to Equation (5). Tis impies tat ˆθ decreases as α increases. Intuitivey, as te cost of te add-on increases, so does te bunde price of te ower-quaity firm. Some consumers woud rater buy ony te base from te iger-quaity firm. On te oter and, te intramargina consumer for te ower-quaity firm, ˆθ, increases wit α. As te add-on becomes 16

18 more costy to provide, it is optima for te ower-quaity firm to excude more consumers wo do not vaue it muc. Consequenty, te segment of consumers wo buy te bunde from te ower-quaity firm srinks. As cost-to-vaue ratio α becomes sufficienty arge, te firm excudes a consumers from buying te add-on, tereby not seing it. 19 Terefore, incentive constraint ˆθ > ˆθ ensures tat te firm ses te add-on in equiibrium, eading to α < 1 2θ θ α (2θ θ) and V > 3 2θ θ 3α w 1. (6) If owever cost-to-vaue ratio α becomes smaer, ˆθ increases wereas ˆθ decreases. Te segment of consumers wo buy te bunde from te ower-quaity firm expands, deriving from two sources. One source of switcers comes from tose wo originay considered ony te base from te iger-quaity firm, and are now drawn to te ower-quaity firm due to its ower bunde price. Te oter switcers originay considered ony te base from te ower-quaity firm, and are now drawn to te add-on because it becomes affordabe. As α becomes sufficienty sma, a consumers wo decided to buy from te ower-quaity firm are wiing to buy te add-on. Te add-on is ten essentiay standard, or free, because a consumers pay just te bunde price. In tis case, ˆθ θ, wic is equivaent to α θ. Constraints (2) and (3) now reduce to ˆθ > θ, eading to V > θ 2θ + α θ 2θ w 2. (7) Te foowing proposition summarizes pure-strategy Nas equiibrium of te game. Proposition If α 1 (2θ θ), tere exists an equiibrium in wic te iger- 3 quaity firm ses te add-on as optiona wereas te ower-quaity firm does not se it; 19 More generay, not seing te add-on is stricty dominated by seing te add-on provided tat α is sufficienty sma. Tis resut is summarized in a emma, anaogous to Lemma 1, in te proof of te next proposition in te Appendix. 17

19 2. If θ < α < 1 3 (2θ θ), tere exists an equiibrium wen V > 1, in wic bot firms ses te add-on as optiona; 3. If α θ, tere exists an equiibrium wen V > 2, in wic te iger-quaity firm ses te add-on as optiona wereas te ower-quaity firm ses it as standard; 4. If α < 1 3 (2θ θ) and V max{ 1, 2 }, tere is no pure-strategy equiibrium. 2.5 Remarks A few remarks are in order. Te teory expains te reative difference in add-on poicies between iger-quaity and ower-quaity firms. Wie a iger-quaity firm concentrates on using an add-on to screen consumers, a ower-quaity firm s poicy is muc more sensitive to te cost-to-vaue ratio of providing te add-on because of its trade-off between screening and differentiation. Internet service as arguaby a very ow margina cost and/or a arge vaue, making cost-to-vaue ratio α very sma. Consumers wo visit ower-end otes aways pay for Internet service. In tis sense, Internet service is essentiay bunded wit room rates, and tus otes are seing it as standard or for free, and quoting ony te tota price. For an add-on wit a arger cost-to-vaue ratio, te add-on price as to be iger to recover te cost, discouraging consumers from buying. It is ten optima for a ower-quaity firm to offer it as optiona. Tis case can expain wy ower-end otes are equay ikey as iger-end otes to offer add-ons suc as aundry or airport sutte services as optiona. It can aso expain wy ower-end airines or cruise ines are equay ikey as teir iger-end competitors to carge for Internet service, because te costs of providing Internet access remain arge based on today s tecnoogy. 20 For an add-on wit a very arge cost-to-vaue ratio, te add-on price may be so ig tat very few consumers coose to pay for it from te ower-quaity firm. Tis case can expain wy ower-end otes are ess ikey to offer amenities suc as 20 Unike otes, airines use ground stations or sateites to provide Internet access on a figt and most cruise ines use sateite tecnoogy to provide Internet access. Currenty in-figt Internet fees range from $10 to $20 per our, and Internet carges on a cruise sip can be as ig as 90 cents per minute. 18

20 mini-bar or room services, compared to iger-end otes wic often se tem as optiona at ig prices. Ceary te competition between iger-quaity and ower-quaity firms for margina consumers wo trade off a iger-quaity base and a ower-quaity bunde is driving te resut. Tis competition is te reason wy a iger-quaity firm is abe to concentrate on price discrimination wereas its ower-quaity riva as to tink more in terms of using an add-on to differentiate. If bot firms are owned by te same parent company, ten it is optima not to aow te two brands to price aggressivey for te margina consumers. One can sow tat in a monopoy mode wit a product ine, under te same set of assumptions, seing te add-on for te ower-quaity brand wi cannibaize profit of te iger-quaity brand. 21 Terefore, absent oter forces, te monopoist wi se te add-on as optiona for te iger-quaity brand but does not se it for te ower-quaity brand. Te teory assumes no orizonta differentiation to focus on te mecanism of vertica differentiation. Rea-word competitions are ikey to invove bot aspects. If two firms are differentiated orizontay, tey wi bot ave an incentive to ower add-on prices. Witout asymmetry generated by quaity difference, owever, te competing firms wi tend to adopt te same poicy. Terefore, orizonta differentiation aone is unikey to expain wy two competing firms diverge in teir add-on poicies. An aternative expanation is tat orizonta differentiations bot at a iger-end market and at a ower-end market can ead to different market outcomes driven by different caracteristics of te two markets. Appying teories of competitive second-degree price discrimination wit orizonta differentiation, under te assumption tat consumers brand preferences are independent of teir preferences for quaity, may predict tat an add-on is sod at te margina cost (Verboven 1999). However, margina costs for Internet service are arguaby sma and simiar at bot te iger-end 21 Due to page imit, te proofs of tis mode and a remaining extensions considered in tis section are not incuded in te appendix but are avaiabe upon request. 19

21 and ower-end markets, suggesting tat otes at bot ends wi offer Internet service as standard, contradicting te styized fact. If te independence assumption is vioated, as Eison (2005) sows, firms wi bunde an add-on wen consumers are ess eterogeneous and unbunde wen tey are more eterogeneous. Te teory can ten expain te styized fact, if consumers are more eterogeneous at te iger-end markets tan at te ow-end markets. However, tis argument reies on te modeing assumption tat ony two types of consumers exist (in terms of teir tastes for a iger quaity), wic eads to te resut tat firms prefer to se an add-on to bot types. Te anaysis of te iger-quaity firm in Section 2.2 impies tat te incentive to unbunde is generay strong provided a sufficient number of types exists. I focus on te simpest setting in wic tere is ony one add-on wit one quaity eve. In reaity, firms can suppy mutipe add-ons (e.g., breakfast, oca cas, or airport sutte), or various quaities of an add-on (e.g., ig-speed Internet access). Tese appications sare te common feature tat consumers wo vaue a iger quaity more sef-seect to buy more add-ons or te iger-quaity eve of te add-on. Te primary intuition of te mecanism appies. For exampe, a-incusive otes are typicay not te most uxurious; ess-tanuxurious otes are more ikey to offer a-incusive services. It is increasingy common tat iger-end otes use tiered pricing to carge for Internet service. Tey offer compimentary Internet access for basic use suc as emaiing but carge for iger-speed Internet or eavy use suc as video conferencing and streaming movies. Tis practice is rarey adopted by ower-end otes. 22 An add-on may evove due to, for exampe, tecnoogy improvement or canging consumer preferences. Tis may reduce te cost of suppying te add-on and/or enance te vaue of te add-on. For exampe, te cost of Internet service as decreased, and te vaue 22 See, for exampe, a recent industry report Hote cains pay WiFi foow te eader (ttp://www. otenewsnow.com/artice/15186/hote-cains-pay-wi-fi-foow-te-eader). 20

22 as increased over time. Based on Proposition 2, it is straigtforward to predict te dynamics of add-on poicies: Coroary 1. As te cost of an add-on decreases, or its vaue increases, over time, te ower-quaity firm s poicy canges from no add-on, to optiona add-on, and eventuay to standard add-on. Reca te tree simpifying assumptions. First, te add-on is omogeneous even toug te firms are differentiated verticay wit respect to te base good. Tis may be a reasonabe assumption for some appications ike Internet service. More reaisticay, te add-on may be asymmetric across firms in terms of cost and/or vaue. For exampe, breakfast may be of iger quaity but it costs more at a 5-star ote tan at a 4-star ote. Second, te margina cost of te base good is assumed equa for bot firms even toug te base quaity differs. Tis assumption may be reasonabe if te quaity premium originates from te fixed costs of investing in te product design of te base good. A 5-star ote, for exampe, can invest in better ocations and views, swimming poos, fitness centers, te costs of wic may be substantiay iger tan tose at a 4-star ote, but ess so for te margina costs. Neverteess, it is more reaistic to aow asymmetric margina costs. Tird, consumers ave te same margina utiity or taste for te base good and for te add-on, making te preferences for te two perfecty correated. It is more reaistic to assume tat consumers ave separate tastes, one for te base good and te oter for te add-on. However, it is not unreasonabe to aow for some degree of positive correation between te two tastes, peraps troug price sensitivity. For exampe, a ess price-sensitive consumer may be wiing to pay more for a more comfortabe room and for Internet service. Eac of tese convenient assumptions can be reaxed witout fundamentay atering te main concusions. 21

23 3 Profitabiity of Add-on Poicies Te focus of anaysis tus far as been on wy and wen a divergence of product poicy arises as an equiibrium outcome. Te anaysis as uncovered te profound effect of vertica differentiation between competing firms. A iger-quaity firm beaves ike a monopoist, wo finds it optima to se an add-on as optiona to screen consumers. A ower-quaity firm faces a trade-off between screening and differentiation. It ses an add-on as optiona in equiibrium ony wen it is not too costy to suppy. Tat seing an optiona add-on is uniateray optima to bot firms does not necessariy impy tat equiibrium profits improve over situations in wic neiter firm ses it as optiona. Tis is because strategic interaction may render te optiona-add-on poicy unprofitabe. To investigate te firms ex ante incentives to impement add-on poicies, I introduce, before firms set price eves, a commitment stage in wic tey can simutaneousy coose weter to commit to a no-add-on poicy or standard-add-on poicy. By committing to a no-add-on poicy, firms do not introduce an add-on, and carge ony for te base good. By committing to a standard-add-on poicy, firms aways bunde te base and add-on, and carge ony for te bunde. Once tey commit to eiter of two poicies, tey are unabe to price te add-on and te base separatey in te second stage of price setting. By not committing to tese poicies, owever, firms retain te fexibiity of seing an add-on as optiona to screen te consumers. Te timing of te game is suc tat bot firms first simutaneousy decide teir commitment coices during te first stage, and ten compete in prices during te second stage, given teir cosen poicies. Tis formuation aows us to compare equiibrium profits wen bot firms se an add-on as optiona to tose wen neiter firm does. By introducing te commitment stage, te mode no onger fits te business environment of te ote industry wic motivates te story. However, oter industries may we be 22

24 consistent wit te modeing assumptions if seing an add-on invoves a arge fixed cost of investment. Te automobie industry seems to be a good exampe. Many advanced features suc as side airbags, GPS navigation, and eater seats require arge investments in production. It may be arder for manufacturers to se tese features as options once investments ave been made. Nine commitment outcomes are possibe in te first stage, and eac can ead to a pricing equiibrium in te second-stage pricing game. To aow equiibrium in wic bot firms se te add-on as optiona, I focus on te case wit moderate add-on cost: θ < α < 1 (2θ θ). Te 3 equiibrium of te fu game is found by first soving te second-stage pricing equiibrium for eac of te 9 commitment outcomes, and ten finding te equiibrium commitment coices taking into account te second-stage subgame outcomes. Te foowing proposition summarizes te equiibrium of te fu game. Proposition 3. Suppose θ < α < 1 3 (2θ θ). Tere exists tresod suc tat wen V >, te iger-quaity firm commits to te standard-add-on poicy, wereas te owerquaity firm commits to te no-add-on poicy in equiibrium. Equiibrium prices are P + = 1 3 ( V + w)(2θ θ) + 2 c, and P = ( V + w)(θ 2θ) c. Te resut tat in equiibrium neiter firm as an incentive to se an optiona add-on is striking. Tis contrasts sarpy wit te insigt from monopoy settings in wic te optiona-add-on poicy is aways profit enancing (weaky). As sown in Section 2, fixing its riva s pricing, eac firm finds it optima to se an add-on as optiona. However, taking into account rivas reactions, firms find temseves trapped in a Prisoner s Diemma; tey can bot be better off to commit not to se an add-on as optiona. To understand wy tis resut arises, it is epfu to examine wat migt ave appened if, under te equiibrium of Proposition 3, firms fai to commit. Wen commitment fais, 23

25 Lemma 1 impies tat it is optima for te iger-quaity firm to separate te base and addon prices, wit te best-response base price given by P (1) = (P + V θ)/2. In response, te ower-quaity firm ses te add-on to tose wo buy ony te base from its riva, inducing tem to switc and get te extra benefit of te add-on. Te firm cooses optima bunde price P +(1) tat responds to te iger-quaity firm s base price P (1), and optima add-on price p (1) tat minimizes te cost of over seing te add-on: P +(1) = 1 (1) (P + c ( V w)θ), and p (1) = 1 (wθ + c). 2 2 Furter, in response to its riva s bunde price, te iger-quaity firm sets optima base price P (2) = (P +(1) + ( V w)θ)/2, wic is ower tan its previous price P (1) given tat α < 1(2θ θ): 3 P (2) P (1) = w (5θ 4θ α) < 0. 8 Te ower base price furter motivates te ower-quaity firm to ower its bunde price. Tis dynamic iterates and converges to an equiibrium in wic bot firms end up being worse off, even toug tey bot se te add-on as optiona eventuay. Te fact tat te two firms end up being maximay differentiated under te two-stage game may bear some simiarity to te same resut tat arises from a styized duopoy mode of vertica differentiation wit ex ante product-design decisions (i.e., firms can coose to invest in V ). However, te resuts of tis anaysis suggest tat even wit te presence of potentia benefits from screening consumers, te maxima-differentiation principe remains dominating. In fact, wat te screening does is te opposite of wat te firms expect; it opens te opportunity for fiercer price competition, tereby urting profits. Te negative resut of te optiona-add-on poicy on profitabiity presents a caenge for firms seing an add-on. In te sort run, firms may be better off seing an add-on as optiona. In te ong run, owever, profits may be damaged if firms are verticay differentiated. Hence, it 24

26 is vauabe for firms to ave commitment powers. For many add-ons in te ote industry (Internet, pone cas, breakfast, etc.), firms ack suc commitment powers because it is quite fexibe for tem to add or remove tese items. For many features in te automobie industry (side airbags, GPS navigation, eater seats, etc.), owever, firms cannot fexiby add tese features once a base mode is buit. Tese features tend to be standard in uxury cars but not in economy cars, a penomenon consistent wit Proposition 3. 4 Unobserved Add-on Prices Tus far, I ave assumed add-on prices are observabe by consumers. Tis is not unreasonabe given tat consumers may earn about prices troug repeat purcases or word-of-mout, and tat in many cases, firms advertise add-on poicies because eiter tey care about reputation or reguations require discosure. Muc of te focus in te iterature, owever, as been on situations in wic add-on prices are unobserved by consumers. For exampe, many consumers do not know about ATM and minimum baance fees wen tey open bank accounts (Cruicksank 2000). Prices of mini-bar items are often unknown to consumers before tey book a ote. In tis section, I expore ow te assumption of unobserved addon prices infuences equiibrium outcomes and firm profits. To tat end, I mode te game as foows: at t = 0, bot firms set prices for te base and add-on; at t = 1, consumers observe ony base prices P and P, and decide wic firm to buy from, and pay te base price; at t = 2, consumers visit te firms tey ave cosen; te add-on price is reveaed and tey decide weter to pay for te add-on. Consumers ave rationa expectations about add-on prices p e and pe. In tis setup, consumers cannot earn about add-on prices by searcing. Toug somewat strict, te as- 25

27 sumption is sufficient to iustrate te probem. In an aternative specification, consumers can incur positive searc costs to discover add-on prices. According to te standard argument by Diamond (1971), even toug searc costs may be very sma, in equiibrium, firms sti enjoy monopoy power ex post after consumers patronize, and tus te add-on is carged at a monopoy price. Te equiibrium outcome is te same as te one presented ere. I examine eac firm s probem in turn and derive te sequentia equiibrium in wic bot firms se an add-on. 4.1 Te Higer-quaity Firm Te iger-quaity firm s probem is anayzed backwards. Suppose a fraction of consumers [ˆθ, θ] decide to visit te iger-quaity firm at time t = 1. Te margina consumer ˆθ is a function of base price P and te tota price of buying from te ower-quaity firm. Among tese consumers, te iger types, θ [ˆθ, θ], buy te add-on if add-on price p e is not too ig. Te intra-margina consumer is given by ˆθ = p e /w. Te firm carges optima price p e tat maximizes add-on profit, π = (θ ˆθ )(p e c). Tis eads to te monopoy price, p e = 1(θw + c), and te equiibrium intra-margina consumer becomes ˆθ 2 = 1 (θ + α). Note 2 tat tis price is independent of te owest-type consumer, ˆθ, as ong as te soution is interior. Terefore, at te beginning period t = 0, maximizing tota profit is equivaent to maximizing base profit, (θ ˆθ )P. Te key observation is tat te iger-quaity firm s probem is essentiay te same as te one wit observabe add-on price. Te add-on price is cosen to maximize ex-post profit given te firm s oca monopoy power. Consumers expect tat even toug te price is unobservabe. 4.2 Te Lower-quaity Firm At time t = 1, remaining consumers θ [θ, ˆθ ] decide to pay te base price to visit te ower-quaity firm. At time t = 2, te consumers observe add-on price p and are faced wit te decision of weter to buy it. Given tese consumers, te firm maximizes ex-post profit, 26

28 π = (ˆθ ˆθ )(p e c) wit ˆθ = p e /w. It is usefu to cange te contro variabe from add-on price p e to intra-margina consumer ˆθ wo is indifferent regarding buying te add-on. Te optima intra-margina consumer is cosen as a function of te margina consumer suc tat ˆθ (ˆθ ) = (ˆθ + α)/2 Taking into account te second-period probem, te firm s probem at time t = 0 is to find te optima margina consumer ˆθ tat maximizes its tota profit max(ˆθ θ)(p ˆθ ( V w) c) (ˆθ (ˆθ ˆθ }{{} ) θ)(w ˆθ (ˆθ ) c). }{{} =p e =P +p e Given te iger-quaity firm s base price P, te best-response for te ower-quaity firm is to coose a margina consumer of ˆθ BR = 2P 2c + (2 V w)θ. 4 V 3w Tis eads to a tota price of P + p e = P of te iger-quaity firm, te resuting equiibrium profie is BR ˆθ ( V w). Combined wit te best response ˆθ = (θ + θ) V (2θ + θ + 2α)w ; P = 6 V 5w 2(2θ θ) V (3θ θ 2α)w 6 V 5w ( V w). Equiibrium outcomes are summarized in te foowing proposition. Proposition 4. Tere exist equiibria in wic te iger-quaity firm aways ses te addon as optiona, wereas te ower-quaity firm s poicy depends on cost-to-vaue ratio α suc tat 1. if α > 1 (2θ θ), ten te firm does not se te add-on; 3 2. if α (θ, 1 (θ + θ)), ten te firm ses te add-on as optiona, wen V > (u) 3 1 ; 3. if α θ, ten te firm ses te add-on as standard wen V [ (u) 0, (u) 2 ], and ses it as optiona wen V > (u) 2. 27

29 Tis proposition reveas tat te interaction between screening and vertica differentiation remains critica even wen add-on prices are unobserved. Te trade-off between te two forces at te ower-quaity firm renders its add-on poicy sensitive to te cost of providing te add-on. Te unobserved add-on price at te ower-quaity firm eads to te od-up probem tat keeps te add-on price ig. As a resut, te owest types refrain from buying te expensive add-on, and ence te firm is ess ikey to se it as standard even wen it is not costy to provide. Te next sub-section furter investigates te impacts of tis od-up effect on equiibrium outcomes and profits. 4.3 Unobserved-price Equiibrium versus Observed-price Equiibrium How does te equiibrium under unobservabe prices differ from te one under observabe prices? To faciitate te comparison, I restrict anaysis to an add-on wit moderate cost so bot firms se it as optiona under eiter scenario. Proposition 5. Consider a moderatey costy add-on suc tat α (θ, 1 (θ + θ)) and a 3 sufficienty arge quaity premium suc tat V > (u) 1. Compared to te observed-price equiibrium, under te unobserved-price equiibrium, 1. te ower-quaity firm as a smaer market sare and ess saes of te add-on; 2. te iger-quaity firm carges a iger base price but te same add-on price, wereas te ower-quaity firm carges a ower base price but a iger add-on price; te tota prices for bot firms are iger; 3. te iger-quaity firm s profit improves, wereas te ower-quaity firm s profit reduces. Te main reason for te difference in equiibrium outcomes and profits is te different effects of te od-up probem on te vertica differentiated firms. For te iger-quaity firm, te od-up probem as no effect because consumers anticipate an ex-post ig add-on 28

30 price carged to expoit te igest-type consumers. Te od-up probem at te owerquaity firm is more subte. Te iger-type consumers at te ower-quaity firm anticipate being ed up at a ig price, and ence wi consider switcing to te iger-quaity firm and buy te base ony, witout paying for te add-on. Consequenty, te market sare of te ower-quaity firm fas. Tis furter reaxes te iger-quaity firm s competitive pressure, tereby increasing its base price. In response, te ower-quaity firm aso increases its tota price. Ceary, te iger-quaity firm benefits from te add-on price being unobserved at te ower-quaity firm. Atoug te ower-quaity firm s tota price increases, its segment of consumers wo pay for te expensive add-on srinks. Eventuay te firm s profit drops. Tis resut suggests tat verticay differentiated firms experience disparate incentives regarding weter to advertise add-on prices. Te iger-quaity firm as no incentive to do so because its iger-type consumers expect te add-on to be expensive because of teir iger wiingness-to-pay. Its ower-type consumers are uninterested in te add-on, so weter te price is advertised is irreevant to tem. Contrariy, te ower-quaity firm as an incentive to advertise to its riva s consumers tat it as a better dea by owering te bunde price. Despite te fact tat te tota price drops, te gains from acquiring new consumers wo originay bougt ony te iger-quaity base good and from persuading more owertype consumers to buy te add-on, make advertising profitabe. Given te incentive to advertise, te equiibrium wi converge to te observed-price equiibrium. 5 Empirica Evidence Te teory is constructed to expain te motivating styized fact tat iger-end otes are more ikey to carge for Internet service, but its impications go beyond te ote industry. Tere are of course oter pausibe expanations for te styized fact. It is beyond te scope of te paper to test eac of tem. In wat foows I provide some suggestive evidence tat is consistent wit te teoretica predictions. 29

31 Prediction. Comparing a monopoy market to a duopoy market wit vertica differentiation wen te cost-to-vaue ratio of te add-on is sma, te teory suggests: (a) tere is no difference between te monopoist and te iger-quaity firm in te vertica duopoy; (b) te ower-quaity firm in te duopoy is more ikey tan te oters to se te add-on as standard. 5.1 Data Te primary data source came from a odging survey study conducted by te American Hote and Lodging Association (AH&LA) every two years. Te surveys present respondents (ote managers) wit a ist of amenities, and ask weter teir properties provide tem. Te ist is compreensive, ranging from in-room and batroom amenities suc as ig-definition TV, coffee makers, and Internet services, to genera services suc as swimming poos, airport suttes, and guest parking. For a few amenities (e.g., Internet service, breakfast, oca cas), respondents report weter tey are provided free. Te surveys aso obtain reevant ote information suc as open dates, and numbers of guest rooms and foors. Te survey popuation incudes a properties in te United States wit 15 or more rooms (more tan 52, 000). 23 I obtained te individua-eve data for te most recent four surveys (2006 to 2012) from te researc company, Smit Trave Researc (STR), wic impemented te study on beaf of AH&LA. Te tota number of respondents for te four surveys was 25, Te company groups otes into five price segments of approximatey equa size based on actua or estimated average room rates: uxury, upscae, mid-priced, economy, and budget. In addition, te company provides numbers of census properties and rooms witin eac zip code. Tere are 163 genera markets and 11, 154 zip codes in te data. To isoate te otes most ikey to be monopoists or verticay differentiated duopoists, I focused on sma markets wit one or two otes witin a zip code. I obtained a dataset from te company tat contained te number of otes for eac price segment witin eac 23 Te overa response rate is 23% wit more tan 12, 000 participants, beieved representative of te U.S. odging industry. 24 Among tem, 65% competed one survey, 24% two, 9% tree, and 2% a four. 30

32 zip code. Tis aowed me to identify monopoy and duopoy markets, and infer te vertica reationsip witin a duopoy market. Tere were 4, 229 observations in tese markets, 1, 441 of wic ad no information concerning in-room Internet service. According to te company, not a properties competed a questions for a variety of reasons. One major reason coud be tat te surveys were ong, fatiguing respondents. Tere is no strong evidence tat woud suggest te pattern of missing information correates wit te otes incentives to offer free Internet service. 25 Anaysis was performed on te remaining 2, 269 observations identified to provide Internet service, eiter free or oterwise. 26 Tere were 1, 285 otes in monopoy markets, 705 otes at te iger end of vertica duopoy markets, and 279 otes at te ower end of vertica duopoy markets. Te 519 otes in orizonta duopoy markets in wic bot otes fa into te same price segment were excuded from anaysis Preiminary Resuts Figure 1 visuaizes te ikeiood of offering free Internet service under various market conditions. 82% of te otes in te monopoy markets provided free Internet service. Higer-end otes in te duopoy markets were equay ikey (81%) to offer Internet free. In contrast, te ikeiood was muc iger for ower-end otes in te duopoy markets: 87% provided free Internet service. Tese descriptive statistics are consistent wit te teoretica predictions. Notice tat te absoute percentages are quite ig across a tree market conditions. Te primary reason is tat tese markets (i.e., zip codes) wit one or two otes are most ikey in suburban or sma towns rater tan in big cities. Tese otes are ess ikey to be uxury or upscae, and ence are more ikey to face upward competition from oter markets. 25 However, it is wort noting tat ower-end otes were ess ikey tan iger-end otes to answer questions on te surveys. 26 I coected additiona pubic data from a major onine trave agency, Expedia, wic ad more compete information, and found very simiar resuts. Tere were 93% of monopoy markets offering free Internet service, not statisticay different from te iger-end otes in duopoy markets (91%), but statisticay ower tan te ower-end otes in duopoy markets (98%). Detais of te data and anaysis are not incuded in te appendix but are avaiabe upon request. 27 Te reativey ig ratio of vertica duopoy to orizonta duopoy is aso an evidence tat otes are often verticay differentiated. 31

33 Furtermore, it is ikey tat many iger-end otes offer basic Internet access for free but carge for eavy uses. Tese otes migt report free Internet poicy even toug tey were practicing price discrimination. Terefore, te observed difference in Internet poicy between ower-end and iger-end otes migt be smaer tan te actua difference, suggesting tat te anaysis is conservative. A number of factors migt ave infuenced Internet poicies. For exampe, many otes ave VIP or cub foors tat target consumers wit iger wiingness-to-pay. Te VIP foors typicay carge customers for iger room rates, but provide additiona benefits tat ikey incude Internet access. Tese otes are ikey not to offer free Internet service to a consumers. Anoter exampe is tat otes vary in terms of number of rooms. A arger size ikey increases setup, maintenance, or abor costs of suppying Internet service, or te cost of impementing price discrimination. Oter potentia confounding factors incude te age, ocation (i.e., airport, interstate, resort, sma town, suburban, or urban), and type of operation (i.e., cain operated, francise, or independent) of a ote. 28 I performed regression anaysis and contro for tese possibe confounds. Te dependent variabe was a binary indicator of weter a ote offered free Internet service. Independent variabes were dummies for tree market conditions: monopoy, ig-end in a vertica duopoy, and ow-end in a vertica duopoy. Monopoy markets were treated as a bencmark group. Te first coumn of Tabe 1 suggests tat (a) te ikeiood of offering free Internet service at a ig-end ote in a duopoy market was not significanty different from tat at a monopoy ote, and (b) te ikeiood was significanty iger at a ower-end ote in a duopoy market in comparison to a monopoy ote. Te second coumn of te tabe reports regression resuts after controing for potentia confounding factors. Concusions remained robust even wen tese confounds were controed. Effects of te confounds varied. As ex- 28 Tere were some otes wit missing information on VIP foor or age. Tese otes were fagged in te regressions. 32

34 pected, otes wit a VIP foor were ess ikey to offer free Internet service. Larger otes were aso ess ikey to offer free Internet service. However, no trend was apparent over te eigt years. 5.3 Higer- versus Lower-end Hotes witin a Duopoy One imitation of te preceding anaysis is tat market-specific factors are not controed. Tis eads to a noisy comparison among otes (e.g., a tree-star ote in Boston is compared to a four-star ote in New York). It woud be usefu to examine weter te two otes in a vertica duopoy beave differenty, a more direct test of te styized fact. To make witinmarket comparison, I restricted attention to duopoy markets in wic bot otes reported teir Internet poicies. 29 Tere were 86 suc duopoy markets. As sown in Figure 3, 74% of te reativey iger-end otes provided free Internet service, wereas 88% of te owerend competing otes provided it for free. A paired t-test suggests tat tis difference was statisticay significant (p = 0.022, t = 2.325). Tis resut suggests tat in a market wit vertica differentiation, te ower-quaity firm is significanty more ikey tan its igerquaity competitor to se an add-on as standard wen it as a very sma unit cost. 5.4 Restricting Anaysis to Upscae Hotes Anoter imitation of te preceding anaysis is tat te patterns found migt be attributed to te differences in price segments. Next I focused on te segment of upscae otes. A ote in tis restricted sampe coud be in te iger-end condition if tere is a mid-priced or beow ote in te same zip code, or in te ower-end condition if tere is a uxury ote nearby. A ote coud aso be te monopoist in a zip code. Tere were 646 observations, of wic 355 were monopoists, 250 iger-end, and 41 ower-end. Figure 2 summarizes te descriptive statistics. Te tird and fourt coumns of Tabe 1 report te coefficients of te ogistic regressions. Te resuts are quaitativey simiar to 29 In te preceding anaysis, te objective was to compare duopoy markets to monopoy markets. It did not require bot otes in te same market reported teir Internet poicies. 33

35 te preceding anaysis. Notice tat te iger-end otes appeared to be more ikey to offer free Internet service tan monopoy otes did. Tis is most ikey because otes in te duopoy condition tend to be in urban or suburban areas, wic potentiay ave more uxury otes forcing tem to free Internet service. Te significance of te difference, owever, was weakened wen contro variabes suc as ocation types were incuded. Restricting te anaysis to te same segment of upscae otes aows us to rue out severa aternative expanations. One is tat iger-end otes face more eterogeneous consumers tan ower-end otes do. Presumaby te upscae otes ave very simiar eves of consumer eterogeneity across different market conditions. Te variation in eterogeneity is unikey to expain te patterns observed ere. It is aso pausibe tat iger-end otes tend to attract consumers wo do not anticipate Internet carges, and tus carge a ig Internet price to expoit myopic consumers. Again, te restriction to upscae otes impies tat te patterns are not attributed to te difference in consumer biases. Anoter aternative argument woud be tat impementing price discrimination costs more at ower-end markets tan at iger-end markets due to efficiency of management, so ower-end otes tend to offer free Internet service (no price discrimination). However, te costs presumaby do not differ substantiay across te upscae otes in te sampe, and ence te cost expanation does not seem to support te observed patterns Concuding Remarks Motivated by te seemingy counter-intuitive penomenon tat iger-end otes are more ikey tan ower-end ones to carge for Internet service, I examine te roe of vertica differentiation in add-on poicies, an eement tat as been eft unexpored in te iterature. Te teory uncovers te differentia roes of add-ons for verticay differentiated firms. Because te firms primariy competing for margina consumers wo trade off a iger-quaity base 30 Te cost expanation is, to some extent, controed by te variabe ote size (number of rooms in a ote) in te regressions. 34

36 good aone versus a ower-quaity base good incuding an add-on, te firm wit te iger base quaity focuses on screening consumers, wereas te ower-quaity firm as to trade off screening and differentiation. Surprisingy, seing an add-on as optiona can intensify competition, because te firms price aggressivey to attract tese margina consumers. Tese insigts are particuary reevant to product poicy decisions tat managers face in many industries. Wen a firm ses an add-on in addition to a primary base product, managers must decide weter tey soud se te add-on separatey from te base as optiona, or se it as standard (i.e., free), or not se it at a. Firms often face competition in te rea-word, bot orizonta and vertica. Ignoring any of te two aspects can ead to miseading poicy recommendations. Tis paper seds some igt on wat product poicies a firm soud adopt in te presence of vertica differentiation. Managers soud evauate teir add-on poicies based on te positioning of teir base good. Tey soud consider weter te base good is differentiated verticay from competitors before designing teir add-on product poicy. Tey soud be cautious regarding weter an optiona-add-on poicy urts profit under competition in te ong run. A number of questions remain unaddressed, and may be wort future investigation. First, te comparative statics impied by Proposition 2 wit respect to te cost-to-vaue ratio of an add-on provide a direction for future empirica work. Detaied data wit exogenous canges in te cost or vaue of an add-on are needed for suc a study. Second, te proposition tat seing an add-on as optiona can urt profits of verticay differentiated firms is an interesting ypotesis to test. Unfortunatey, te data used in tis paper were unsuitabe to test it. Future empirica researc into tis topic is wort exporing. Tird, te teory focuses on pure vertica differentiation, assuming away orizonta differentiation. In reaity, firms are often differentiated bot verticay and orizontay. Furter researc aowing for bot aspects is interesting. 35

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39 Figure 1: Vertica Duopoy vs. Monopoy in Sma Markets Figure 2: Vertica Duopoy vs. Monopoy in Sma Markets (Upscae Hotes) Figure 3: Higer- vs. Lower-end Witin a Vertica Duopoy 38