Making Sense of (Ultra) Low Cost Flights Vertical Differentiation in Two-Sided Markets∗ Luigi Serio†

Piero Tedeschi‡

Giovanni Ursino§

July 15, 2016

Abstract The business model of low cost carriers is now well-established and accounts for a large share of western civil aviation, particularly in Europe. To understand why it has proven so successful, we develop a theoretical model that exploits the two-sided nature of flights as connectors of supply and demand for goods and services other than traveling itself across physical space. Carriers offer flights of different quality and may sign agreements with suppliers of goods and services at the destination so as to subsidize and foster demand from the carriers’ travelers as in standard two-sided markets. Customer-travelers care about home and destination consumption and about the flight’s quality. Hence, beyond the thickness of the connected sides of the market, the quality of the airline-platform has an intrinsic value to travelers. We show that only low-income travelers fly with low cost airlines, while no-frills carriers are more likely to act as a platform than legacy airlines. We study how the degree of substitution between home and destination consumption affects the equilibrium market structure of the airline industry. JEL Classification Numbers: L1, L2 Keywords: vertical differentiation, two-sided markets, air travel, low cost flights

∗

We thank the editor of the Business Strategy Department at Management Science, Bruno Cassiman, an anonymous Associate Editor and two reviewers. We thank Bruno Jullien for valuable comments as well as seminar attendants at TSE. † ICRIM, Universit` a Cattolica del Sacro Cuore, Milan. ‡ DEFIN, Universit` a Cattolica del Sacro Cuore, Milan. § DEFIN, Universit` a Cattolica del Sacro Cuore, Milan. Corresponding author: [email protected].

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Introduction

Almost all Europeans and most Americans are familiar with low cost flying. While low cost airlines exist since the ’70s,1 the phenomenon has constantly grown. At least since the late ’90s it has reached a mass market status and is now considered an established but still growing industry. This is particularly true of the European commercial aviation: with the emergence of budget airlines in the late ’90s the growth trend of established network carriers has stopped. Today, full service carriers still handle approximately the same demand for air travel as in 2000, while their relative market share has decreased. By contrast, low cost carriers have grown at high double digit rates and captured large parts of the market. They expanded their market share from 5% in 2001 to 32% in 2008. In some European countries, low cost carriers even dominate the market. In Spain, they account for 50% of the total international capacity offered, in Poland for as much as 52%. Also in other economies, budget carriers have been able to expand their market share in an impressive way over the last decade, which puts severe pressure on established network carriers. In Germany, Europe’s largest economy, low cost airlines operate 29% of international and 44% of domestic flights.2 While low cost companies were growing steadily, the 2000s witnessed a sharp increase in the demand for air travel in Europe, which jumped by around 47% between 2000 and 2008.3 To some extent this may be due to a higher flying frequency for some travelers but that does not explain the entire picture. The evidence suggests that the entrance of low cost carriers into the industry has made access to air travel possible to lower-income people, for whom traveling with established carriers is not affordable.4 A considerable share of the new traffic is made of tourists traveling within Europe.5 At least until recently, attracting this ‘latent demand’ has been the core business of budget airlines. This has been possible even though the airline industry as a whole was undergoing a severe crisis after the end of the “golden 90s”. In fact, low cost airlines have bypassed tough competition with incumbents by creating uncontested market space. To achieve this result they have attracted low-income customers not served by established carriers, de facto opening a new-market segment of the air travel industry. The positioning strategy just illustrated is built on at least two pillars: cost-containment and revenue enhancement. As the name suggests, low cost carriers rely heavily on cost-containment, which, among 1

During the ’60s and the ’70s Loftleidir launched the first low fare service across the North Atlantic flying into Luxembourg “the heart of Europe.” The airline became very popular among college students traveling abroad and soon became known as “The Hippie Airline” flying, among others, former US president Bill Clinton. The first fully low cost airline is generally considered to be the American company Southwest which launched in 1971, with the then revolutionary concept that you could lower the cost of ticket prices by eliminating some of the extras and therefore save passengers’ money. 2 Future Scenarios for the European Airline Industry, a 2010 Report of the Center for Scenario Planning, Roland Berger Research Unit and HHL - Leipzig Graduate School of Management. 3 See Footnote 2. 4 “In the 1950s flying was a privilege enjoyed by only the wealthiest. The costs of flying were simply too high for most ordinary folk. In 1952 a London-to-Scotland return flight would set the average Englishman back a week’s wages; a trip to New York might require saving up for five months. But in 2013 flying is a mass market, due in no small part to the growth of “no-frills” airlines offering flights at very low prices.” from The Economist website at www.economist.com/blogs/economistexplains/2013/10/economist-explains-13. 5 See, e.g, the UK Civil Aviation Authority report “Demand for Outbound Leisure Air Travel and its Key Drivers” (December 2005) available at www.caa.co.uk/docs/5/erg elasticity study.pdf.

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other things, allows them to charge budget fares. Hence, the management literature has extensively investigated the cost-containment strategy at the basis of the budget lines’ business model. While the accent was mostly placed on the operational choices, there are many factors allowing for substantial cost-savings. However, no single driver has been identified as the main determinant of the competitive advantage of low cost companies. As we will clarify shortly, this paper abstracts from operational costs as it highlights a new channel through which a budget airline can increase its profitability. Incorporating cost-saving strategies would strengthen our results but would divert the reader from our intended focus. We therefore refrain from modeling operational costs in this paper. The ultimate success of the low cost business model relies not just on low costs, but on high margins: enhancing revenues also plays an important role in budget airlines strategies. This aspect has been less studied, although the management literature has highlighted how leveraging on the efficiency of electronic markets has been essential to implement profit-enhancing pricing policies. Revenues are also optimized via pay-for-frills policies and similar strategies that allow airlines to discriminate among travelers based on their willingness to pay for extra services. While, again, we do not focus on this type of strategy, our results are consistent with the idea that revenues are raised by increasing per-passenger margins. The aim of this paper is to show that there exists a third pillar to the positioning strategy of low cost carriers, which, to date, has been exploited only by Ryanair, and, we argue, this is at the basis of its uncontested leadership. Indeed, the recognized champion of the low cost flights industry is Ryanair, which alone has a market share of short-haul passengers in Europe around 14%.6 Such an impressive score is accompanied by announcements like that released by Ryanair chief executive Michael O’Leary in November 5, 2007: “It’s our ultimate ambition to get to a stage where the fare is free.”7 That interview focused on cost-containment as Ryanair was about to introduce a clamping down of the pay-for-frills policy with the doubling of check-in, as well as baggage, fees. Indeed, cost minimization is the backbone strategy of every low cost airline: saving on ‘frills’ to lower prices and attract low budget travelers. However, Ryanair’s average fare in 2013 (¤48) was by far the lowest, with the second cheapest (Easyjet, ¤82) charging 71% higher.8 This allows Ryanair to define itself as a (ultra) low cost carrier. Can this performance be explained just as a result of cost reduction? Clearly not. A distinguished feature of its business strategy is the way Ryanair deals with its more than seventy ‘bases’ around Europe.9 Among the airports from which Ryanair operates, the bases are those hosting the carrier fleet. More importantly, most bases are almost exclusively operated by Ryanair, which is by far the dominant carrier of the airport. This is not by chance: Ryanair carefully chooses its bases targeting minor airports situated not far from attractive locations. The small size of such airports — at least before the arrival of Ryanair — grants the carrier a bold stance when bargaining the terms of its operations. The 6

Ryanair share of seats among all carriers in period April 29 – May 5, 2013. See www.centreforaviation.com/analysis/ ryanair-europes-lowest-cost-producer-wins-again-reporting-record-profit-of-eur569-million-110543. 7 See www.dailymail.co.uk/news/article-491907/No-cost-flights-Ryanair–passengers-incur-costs.html. 8 Source: latest published company year end information, as reported in the Full Year Results 2013, Ryanair. 9 The opening of the 71st base (Bratislava) was announced on Nov 13, 2014 on the Ryanair Website. In December 2013 Ryanair had 57 bases according to the Full Year Results 2013.

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convenient location grants Ryanair a sustained demand, perhaps because it is near an important touristic attraction. The strategy described so far is just an aggressive cost minimizing/demand enhancing one. Ryanair, however, is the only carrier that goes (way) beyond that: realizing that many of its passengers are leisure travelers and likely customers of destination goods and services (hotels and touristic services, local food products, fashion garment, etc.) the carrier actively exploits its role as connector between demand and supply to extract part of (and sometimes most of) the potential gains from trade. In fact, to some extent all air carriers build networks that create exchange opportunities — i.e., network externalities. But only Ryanair actively exploits this platform side of air travel — the third pillar of Ryanair successful positioning strategy! To see how the third pillar works, one has to look at the contracts agreed to by Ryanair when the airline opens a base. Such contracts10 can be signed with the companies managing the airport but most often involve local authorities, business representatives such as chambers of commerce and, more generally, ‘destination stakeholders’. Some examples of destination stakeholders are: the Oriocenter Shopping Center11 in Milan Orio al Serio, Airgest and Regione Sicilia in Trapani Birgi, Regione Puglia in Brindisi, Catalu˜ na and Costa Brava hotels in Reus and Gerona,12 etc. The agreements between the (ultra) low cost carrier and destination stakeholders usually stipulate that the latter pay Ryanair an amount varying with the number of passengers that the carrier commits to fly to the destination. For instance, Trapani paid ¤20 million in five years and passengers soared from 533 thousand in 2008 to 1.2 million in 2012.13 In some cases the contractual relationship is mutually advantageous and sustainable, but it sometimes happens that the terms disproportionately favor Ryanair: while, for instance, Orio al Serio and Brindisi are success stories, the airport of Verona — which paid the carrier ¤24/passenger until recently — came close to bankruptcy.14 This paper is about the economics underlying the business model of Ryanair. It aims at explaining the success of the (ultra) low cost carrier, its impact on the industry and the consequences for the consumption habits of million of low to mid-income people. It does so by recognizing and modeling the unique feature of Ryanair’s strategy: not just competing on quality as a normal low cost carrier, but actively exploiting the network externalities inherent in moving people across markets. Ryanair acts as a platform connecting demand and supply located in different countries and extracts part of the generated surplus to keep its fares at otherwise unprofitably low levels. It therefore competes on quality with other carriers but, at the same time, generates profits by selling its platform services in many two-sided markets around Europe, each associated to a specific network externality characteristic of each route. 10 These contracts are extremely heterogeneous and often not public. Nonetheless they have attracted much attention as the European Antitrust has investigated into some of them suspecting they masked state aids. The ‘soft’ evidence mentioned in the following paragraphs is mostly the result of investigative reports by local journalists and/or specialized press. While mostly unofficial, this body of suggestive evidence is certainly pointing at a substantiated reality. 11 More information at www.oriocenter.it. 12 See for instance www.elperiodicomediterraneo.com/noticias/castellon/cataluna-paga-46-millones-ryanair-traer-turistas -reus-girona 728694.html. 13 For concise information on Italian airports dealing with Ryanair see https://it.finance.yahoo.com/foto/gli-aiutini-distato-a-ryanair-slideshow. 14 See Footnote 13.

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We deem natural to model the airline industry as a vertically differentiated duopoly in which two airlines, a low quality (low cost) carrier and a high quality (full service) one, compete to attract potential travelers on a given route as in standard models. Customer/travelers have different income levels and care primarily about the flight quality and, secondly, about goods consumption. They can purchase goods both at home and, if they travel, at the destination, where they can source from a number of shops. These destination businesses are collectively represented by a local stakeholder (chamber of commerce, regional council, shopping mall, etc.). We depart from the standard vertical differentiation setup assuming that carriers have the opportunity to propose a contract for operating the route to the local stakeholder. The latter can strike a deal with just one carrier — that is, contracts are exclusive. The destination stakeholder, however, sells goods and services to the travelers brought to the destination by both carriers. Hence, while traveling with either carrier generates positive network externalities on travelers — i.e., being able to purchase at the destination — only one carrier can price on both sides of the market as a proper platform, whereas the other prices just on the traveler’s side. Put differently, exclusivity implies that only one carrier can internalize the network externalities it generates. We study and compare three scenarios: a standard competition benchmark in which no carrier deals with the local stakeholder, one in which the stakeholder deals with the full service carrier and one in which he deals with the low cost carrier. The travelers in our model purchase with probability one from each destination shop regardless of which carrier they fly with, a standard assumption in the two-sided markets literature. This simplifies the analysis. In fact, casual empiricism suggests that carriers actively direct travelers to destination businesses, typically tailoring their marketing strategies to their clientele and thereby affecting the probability with which travelers purchase. While our model abstracts from these issues, we notice here that our results would be otherwise strengthened as discussed at the end of Section 4.4. We find that the optimal contract between the local stakeholder and a carrier is a two-part tariff prescribing a per-passenger payment to the carrier in exchange for a fixed amount to the stakeholder. Not surprisingly, the stakeholder always finds it optimal to deal with a carrier rather than not signing any contract — i.e., the competition benchmark is never an equilibrium when contracting is possible. More importantly, we show that the overall demand for air travel depends on the level of the low cost carrier airfare and increases when the latter decreases. Indeed, we find that flights are cheaper and demand is larger when a carrier deals with the stakeholder and, in particular, demand is largest when the carrier is a low cost one, confirming the evidence from the emergence of low cost airlines and passengers’ data. Moreover, travelers flying low cost are cash-constrained — i.e., they would prefer to travel on a full service flight — while very low-income consumers prefer not to fly at all. In essence, the model shows that two-sided pricing allows the platform-carrier to subsidize passengers reducing the price of flights on the intensive margin. This, in turn, increases demand from cash-constrained consumers on the extensive margin, which effectively generates a new market segment. We then endogenize the market structure. We allow the destination stakeholder to bargain separately with both carriers and to select the most convenient exclusive deal. We prove that the equilibrium market structure always entails exclusive dealing with the low cost carrier, which is superior both to 5

the competition benchmark and to dealing with the full service carrier. This finding depends on how strongly the extensive margin is affected, that is how many more passengers are attracted to the route. The extensive margin clearly depends on the pricing of the low cost carrier only. If the local stakeholder deals with the low cost, the latter internalizes the externality substantially, lowering its airfare. By contrast, when the deal is with the full service carrier, the low cost competitor lowers its airfare only as a strategic response to the lower fares of the full service. It turns out that the former effect is stronger than the latter. Hence, the most efficient contract is that with the low cost carrier. Our paper therefore rationalizes the evidence that contracts between airlines and local stakeholders are, in fact, used only by Ryanair, a low cost airline. On the contrary, no conventional carrier adopts a similar strategy. We further show that low cost-stakeholder contracting also maximizes consumer welfare and carriers profits. Finally, we show by numerical simulations that when dealing with the stakeholder the profits of the low cost carrier are larger the less substitutes domestic and destination goods are. Hence, the profits of the low cost carrier from operating the route through the contract described here are higher when destination businesses offer goods or services not available at home. This contributes to explaining why Ryanair operates certain routes through the contract with the stakeholder while others are operated in a standard regime. It is worth noticing that, as a matter of fact, the first and most profitable route operated in Italy by Ryanair is to and from Orio al Serio, where a contract is in place with the above mentioned Oriocenter shopping center. It turns out that the latter offers a great opportunity to many low income travelers to purchase Italian fashion garment at affordable prices not easily available outside Italy.15 Similarly, public authorities in Catalu˜ na subsidize Ryanair for flying travelers to hotels and resorts offering holidays in the Costa Brava beaches, obviously not an easy substitute for most NorthEuropeans looking for some rest on sunny shores.16 The economic analysis of vertical differentiation in two-sided markets that we perform in this paper is valid well beyond the case of Ryanair. While the model framing best matches the air travel industry, its essential characteristics are more general. Our analysis applies to any industry in which: i) there is some element of (vertical) differentiation in a primary market and consumers value quality; ii) sellers provide a service that generates positive network externalities to third parties; iii) the innovating firm serves the market segment that generates the largest externalities; iv) the pricing of these externalities allows the innovator to cross-subsidize its customers, thereby reducing prices and expanding demand via the extensive margin in the primary market. The paper is organized as follows: related literature is discussed below. Section 2 presents the model. Section 3 analyses optimal consumer’s behavior, studies monopolistic competition among destination shops and derives flight demand as a function of the carrier pricing decisions. Section 4 studies the standard competition scenario, the scenario in which the low cost carrier deals with the local stakeholder and that in which the full service does, and compares the equilibrium outcomes. Section 5 characterizes the market structure that emerges endogenously in equilibrium and its determinants. Section 6 discusses 15 16

See for instance http://archiviostorico.corriere.it/2004/ottobre/03/aereo Londra con euro Orio co 5 041003019.shtml. See Footnote 13.

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our findings in light of two popular theories of the management literature — disruptive innovation and blue ocean strategy — and briefly illustrates the Metro free press case to confirm the generality of our analysis. Section 7 concludes.

Related Literature Our work touches several strands and different bodies of literature. Management scholars have studied heavily the airline industry (see Doganis (2006) and Zhang and Czerny (2012) for comprehensive reviews) and some authors have focused on low cost airlines in particular. For instance, Franke (2004) puts the accent on the many cost benefits underlying the low cost carriers’ strategy that allow them “to deliver 80% of the service quality at less than 50% of the cost” of established network carriers. However, he concludes that no single factor lies behind the cost-related competitive advantage of low cost carriers. Other authors, both management and economics scholars, have focused on revenue enhancing strategies, mostly pricing. In particular, both Malighetti, Paleari, and Redondi (2009) and Alderighi, Nicolini, and Piga (2015) study the pricing behavior of Ryanair and show that carefully designed yield management strategies substantially boost the carrier’s revenues. As previously pointed out, our work does not contribute to either of the above mentioned strands of the literature and a more in-depth review of the literature in this area is beyond the scope of this paper. Our objective is to shed light on the economics behind the extremely low fares charged to passengers by Ryanair. Indeed, our results closely track the strategy and market outcomes observed in practice. From a theoretical point of view, they are made possible by the combination of vertical differentiation and two-sidedness into a single framework. The literature is vast on both aspects and reviewing it goes beyond the scope of this work. See, however, Rochet and Tirole (2006) on two-sided markets and Tirole (1988) on vertical differentiation. Our work lays at the intersection of these strands of the literature. To the best of our knowledge, no other work shares a structure similar to ours. However, following Armstrong (2006), many authors have studied competition among networks and the idea that competing platforms may differentiate is not novel. Although we do not model network competition since only one carrier prices both sides of the market, it is worth mentioning those works that have studied differentiation among competing networks. Argenziano (2008) presents a model in which two ex-ante identical networks compete to attract agents who have incomplete information about the networks quality (a common value) as well as heterogeneous (private) valuations about the goods on sale. She finds conditions for unique equilibria to emerge and shows that networks are suboptimally differentiated because consumers fail to internalize externalities due to the incomplete information structure of the model. Our model differs in several ways: carriers’ qualities — i.e., the common value — are common knowledge; consumers are heterogeneous with respect to their income levels, not preferences; both carriers compete on the air travel market but only one uses platform pricing. Gabszewicz and Wauthy (2014) model competition between two vertically differentiated platforms — while Ribeiro, Correia-da-Silva, and Resende (2014) build on their framework. In these works a platform’s quality is endogenous and is higher the larger the

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market share and the associated network externalities. Their platforms compete to attract users as in classical models and have no value per se. On the contrary, as in our framework consumers care directly about it, airlines compete on the intrinsic quality of their flights, independently of network externalities. These are internalized on top of and interact with the standard competitive environment of a vertically differentiated duopoly. Finally, a growing body of literature models airports as platforms connecting airlines travelers on on side to retailers located at the airport on the other. Ivaldi, Sokullu, and Toru (2015) argue that airports should be considered as two-sided platforms because of network externalities between airlines and passengers rather than vertically integrated businesses with passengers as final consumers, a common modeling assumption in the literature. Yet, they empirically show that the major U.S. airports do not internalize these externalities. On the theoretical side the model developed by Flores-Fillol, Iozzi, and Valletti (2015) is close to ours in several respects — e.g. the quasi-linearity of travelers’ utility function —, yet different along fundamental dimensions. In their model, airports charge landing fees to airlines and choose the market structure of destination businesses — i.e., the number of concessions for commercial activities in the airport. They study the optimal degree of differentiation of retail activities as a function of whether or not (and to what extent) travelers correctly foresee their surplus from retail activities located at the airport. Our work differs from these studies: firstly travelers in our model enjoy surplus not only from airport located retailers, but from a possibly wider set of amenities; secondly and consequently the platform in our model is the carrier and not the airport; thirdly we model competing platforms; fourthly platform-carriers are vertically differentiated along the primary good dimension (the travel service); and last travelers have perfect foresight and anticipate the utility they can derive from consumption at the destination.

2

Model

Players. Two airlines must decide how to operate a route to a given location providing services of possibly different qualities. As in a standard vertical differentiation model in equilibrium qualities will be different: we call Full Service the airline providing high-quality standards and we refer to the other as a Low Cost carrier with a no-frills policy.17, 18 Airlines are indexed by J ∈ {F, L}. Carrier F offers a quality QF and charges an airfare TF per-passenger while carrier L offers quality QL < QF and charges TL . For tractability reasons we take quality levels as exogenous, QL is normalized to 0 without loss of generality, and we assume that carrier F sustains no cost for meeting quality standard QF .19 17 By flight quality we mean the bundle of all the features which make traveling comfortable, efficient and enjoyable, from flight frequency to leg space, from catering aboard to lounge services, etc. 18 Defining what a “low cost carrier” means is not an easy task, even more so now that the industry has been populated by many “hybrid” airlines. We refer to Alamdari and Fagan (2005) for an interesting discussion of the original low cost business model of Southwest (1971) and how it has evolved through time both at Southwest and for nine other major low cost carriers in the USA and EU. 19 While the model is robust to the introduction of a cost of quality — as long as it keeps the Full Service carrier in business —, the zero costs assumption simplifies the analysis without sacrificing any intuition. The only drawback is that

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Located near the destination airport are M businesses. They could be hotels, museums, etc. but for the remaining of the paper we will call them shops and, to name them collectively, we will adopt the Mall example presented in the introduction, using alternatively the terms shops and Mall. Each traveler k may buy a quantity qik ≥ 0 of the good provided by shop i at price pi . Following the standard approach in the two-sided markets literature, we assume that travelers have access to the same set of shops regardless of the carrier they fly with.20 Shops are naturally interested in airlines decisions insofar as passengers are potential buyers. In order to attract buyers, the shops — which, for the sake of simplicity, create the ‘Mall’ to deal with airline companies — may be willing to subsidize airline J with a transfer SJ per traveler taken to the destination.21 To partially compensate for this, optimal contracts between airlines and the Mall may have a two-part tariff structure, prescribing a fixed transfer ZJ to the Mall, which is evenly split among shops. In this case each shop subsidizes airline J with a payment sJ = SJ /M per traveler carried by airline J and receives a fixed payment zJ = ZJ /M .22 Each shop has a constant average cost c > 0. Beyond goods at the destination, whether he flies or not, a potential traveler k may consume a quantity q0k ≥ 0 of a num´eraire good at home at the normalized price p0 = 1. Note that we do not model the relationship between the Mall and individual shops. The Mall contracts with the carriers on behalf of the shops and its profits are the sum of shops’ profits. Shops set retail prices non-cooperatively given the contract agreed upon by the Mall. Shops are identical and obviously cannot strike exclusive deals with a carrier. Hence, it is immediate to see that an individually rational shop accepts the Mall-sponsored contract that obviously takes into account the participation constraint of the shop. Finally, there is a unit-mass of travelers, indexed by k, endowed with a uniformly distributed income Ik ∼ U [0, 1]. Travelers use all their income for flying and buying goods — i.e., they derive no utility from money per se and care only about the flight’s quality and shopping at home and at the destination. Building on Dixit and Stiglitz (1977), the utility function of traveler k when flying with carrier J is a nested CES on consumption goods with the addition of a quasi-linear component on flight’s quality23  ϕ UJk (QJ , q0k , q1k , ..., qM k ) = QJ + q0k +

M X

! ϕρ  ϕ1 ρ qik



J = F, L

(1)

i=1

the profits of the Full Service carrier are trivially higher than those of the Low Cost carrier in equilibrium. 20 Assuming that the positive network externality (i.e. access to shops) is provided to travelers by both carriers plays against us, making our result more difficult to obtain and therefore stronger. But it also allows us to model a variety of cases, ranging from airport-pair markets to city-pair markets in which carriers fly to the same city with more than one destination airport. For instance, keeping with the example of the introduction, the Orio al Serio airport in Bergamo serves Milan along with the city airport Linate and the major intercontinental airport Malpensa. 21 When public local authorities provide these subsidies, they “behave like a market economy operator” and cannot therefore be considered state aid. However we are aware that the issue of state aids is still unsettled — see EU memo at http://europa.eu/rapid/press-release MEMO-14-544 en.htm. 22 In most of the analysis we will refer to contracts specifying the Mall-level transfers SJ and ZJ , but, particularly when dealing with shops’ optimal behavior and occasionally elsewhere, we will use the shop-level notation sJ and zJ . 23 See Flores-Fillol, Iozzi, and Valletti (2015) for a similar quasi-linear specification.

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where the CES parameters ϕ ∈ (0, 1) and ρ ∈ (0, 1) reflect consumers’ taste for variety: between home and destination goods, ϕ, and between goods at the destination, ρ. The k subscript denotes the choice of consumer k endowed with income Ik . It is natural to represent the utility of a consumer who does not travel by setting to zeroes all the arguments of (1) but the home good and write it as a function of the num´eraire good alone k UN (q0k ) = q0k .

Timing. The the airline industry game is played as follows: t = 1 Carriers set the quality levels QJ ∈ {0, QF }. t = 2 Carriers propose contracts (sJ , zJ ) to the Mall; the Mall decides which contract to accept, if any. t = 3 Carriers simultaneously compete on fares TJ . t = 4 Shops set prices pi , i = 1, .., M . t = 5 Consumers decide whether to fly and the amount of goods to purchase.24 Equilibrium concept and strategies. The game is a sequential game with complete information and the natural solution concept is Subgame Perfect Nash Equilibrium. We focus on pure strategies. The actions available to carrier J are {QJ , TJ , SJ , ZJ } with QJ ∈ {0, QF }, TJ , SJ and ZJ non-negative. The action space of each shop is {‘Accept (sJ , zJ ) ’, ‘Not Accept (sJ , zJ ) ’, pi } for J = F, L and i = 1, ..., M with pi ≥ 0. Finally, traveler k’s actions are {‘Not fly’, ‘Fly with F ’, ‘Fly with L’, q0k , ..., qM k }.

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Consumers’ and Shops Behavior

Consumer’s behavior. Our equilibrium analysis proceeds by backward induction, starting from the consumer’s decisions. There are (at most) three types of consumers: those who don’t fly, those who fly with F and those who fly with L. Consumers who don’t fly spend all their income for the home good k = I . The consumption decisions of those who fly are less straightforward. Let’s thus and get utility UN k

study the purchasing choices at the destination of a traveler who has decided to fly with airline J. Given shops’ prices, the consumer maximizes (1) subject to the budget constraint Ik − q0k − TJ −

XM

24

i=1

pi qik ≥ 0.

(2)

Owing to monopolistic competition and CES utility, the price set by a single shop only depends on substitution elasticity and marginal cost — see equation (11). Hence, we could have assumed that shops set prices at any time. We assume they set price in t=4 mainly for clarity of exposition.

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The optimal demand of consumer k for the num´eraire and destination good i is Ik − TJ 1 + P 1−τ P σ−τ Ik − TJ = pσi 1 + P 1−τ

(3)

q0k = qik

where P ≡

P

M 1−σ i=1 pi



1 1−σ

i = 1, ..., M

is the “destination price index” and σ =

(4)

1 1−ρ

> 1 and τ =

1 1−ϕ

> 1 are

the elasticity of substitution between goods at the destination and between home and destination goods respectively. Clearly, the quantity of both home and destination goods purchased by traveler k increases with his income net of traveling costs (‘net income’ hereafter). Combining (1), (3) and (4), the utility of traveler k flying with J is UJk = QJ + where Π ≡ 1 + P 1−τ




1 1−τ

Ik − TJ , Π

(5)

is a “global price index” including both the home price (11−τ ) and the price

index of destination goods (P 1−τ ) and does not exceed 1.25 Naturally, UJk increases in the net real income,

Ik −TJ Π ,

and in the flight’s quality, QJ — which, in fact, is the utility derived from the quality of

airline J given the quasi-linearity of (1). Having characterized goods consumption choices of consumer k, let’s now consider his flying decisions. Let’s begin with the choice to travel altogether. He will travel if, for at least one airline J, it holds k UJk ≥ UN

⇐⇒ Ik ≥

TJ − ΠQJ , 1−Π

(6)

while he will not travel if (6) is never satisfied. The flying condition above is stricter the higher the cost of flying, TJ , while it is met more easily when flying provides a higher quality, QJ . More interestingly, the right hand side of (6) increases with Π if, and only if QJ /TJ — the flight’s utility per euro spent on flying — is smaller than one, and vice-versa. The intuition is as follows: when Π increases, destination prices P increase, while home consumption and flight fares become relatively cheaper. Hence, a marginal traveler reallocates consumption to the good or service that provides the highest utility per unit of money. If he decides not to fly, the marginal utility of money spent in the home good is 1 as compared to the marginal utility of money spent in flying, QJ /TJ . When the latter exceeds 1, then an increase in Π makes the marginal traveler strictly prefer flying, while he stops traveling under the opposite condition. Hence, the number of travelers increases with Π when QJ /TJ > 1 and decreases otherwise. Let’s now assume for a moment that (6) holds for both carriers and consider the choice a traveler 25

It is easy to show that, for τ > 1 and P > 0, condition Π ∈ (0, 1) holds. See Lemma 2 for further details.

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has to make about which airline to fly with. Traveler k will fly with a Full Service carrier if UFk ≥ ULk ⇐⇒ QF ≥

TF − TL . Π

(7)

Condition (7) does not depend on individual income. Hence, it is a condition for the existence of the demand of Full Service flights and we assume it holds throughout.26 Its interpretation is straightforward: as long as the extra cost of flying with a Full Service airline, TF − TL , is not too large, travelers prefer a more comfortable flight. However, the condition is harder to be satisfied when the price index is low: in fact, when this is the case, the marginal utility of money spent at the destination is high. Hence, the Full Service carrier has to provide a high quality or charge a low fare to attract travelers. Indeed, if prices are low enough, travelers may prefer to save money on flight extra quality in exchange for goods consumption at the destination. Thus, a quality that is acceptable for high shop prices may become unacceptable when prices are low enough: flight quality and goods purchases are substitutes. As noted above, condition (7) does not depend on income: if it holds, whenever they can afford it, travelers prefer to fly with a Full Service airline. Moreover, it implies that the income level satisfying the flying condition (6) is lower for the Low Cost carrier than for the Full Service carrier. This gives rise to a simple assignment of optimal flight choices based on income: low-income consumers (with Ik <

TL 1−Π )

prefer to stay home; those with a higher income want to travel and wish to fly with the Full Service airline, but a part of them — say the middle class (with

TL 1−Π

< Ik < TF ) — cannot afford it, while

the remaining consumers — the upper class (with Ik > TF ) — fly with the high quality company. The market demand for flights just described — which we denote as DF ≡ 1 − TF and DL ≡ TF −

TL 1−Π

for

Full Service and Low Cost flights respectively — is illustrated in Figure 1. Figure 1: Optimal flight choices and Income No Fly Ik = 0

Fly with L (DL ) TL 1−Π

Fly with F (DF ) TF

Ik = 1

While the Full Service carrier demand is fully determined by a mere cash constraint, the lower bound of the Low Cost carrier demand is pinned down by a preference constraint and depends in a more nuanced fashion on the goods consumption preferences through the price index Π. As it will be clear later, this has deep implications on the pricing policies and on the capability of the Low Cost carrier to exploit its platform nature. 26

In particular, we assume that the exogenous quality is high enough to avoid corner solutions when carriers set airfares.

12

Shops pricing. We now proceed to analyze the optimization problem of destination shops. We assume that they engage in a standard monopolistic competition framework. This seems a natural choice given the problem modeled here: in fact, on the one hand we need a market structure that generates some surplus to the shops to properly model a two-sided market; on the other hand we want to focus on the strategic interaction between the Mall and the carriers abstracting from the subtleties of shops competition. The demand for shop i is obtained integrating the optimal consumer choice (4) over the income distribution and is qi = where I˜ ≡

P σ−τ I˜ pσi 1 + P 1−τ

(8)

Z

Z

(Ik − TL ) dIk

(Ik − TF ) dIk +

(9)

DL

DF

is the travelers’ aggregate net income, i.e. the income not spent by travelers in flight tickets that is available for purchasing goods. The overall demand for shop i, qi , decreases as pi increases while it ˜ increases. The latter, in turn, clearly increases increases when the overall passengers’ net income, I, when the ticket of the Low Cost airline, TL , decreases, as more passengers can afford to travel (extensive margin) and those who already fly spare some money (intensive margin). As to the effect of a change in the fare of the Full Service airline, it is non-monotonic. In particular, because income is uniformly distributed, the airfare that maximizes net income is exactly midway between the maximum available income and the Low Cost fare. Given the Mall and carriers contracting decisions, shop i sets price pi to maximize profits n o max (pi − c) qi − sJ DJ + zJ , pi ≥0

(10)

where qi is given by (8) and the contract (possibly) agreed to with carrier J is defined by a variable part, sJ , and a fixed one, zJ . The optimal price is the same for all shops and equals p=

σ c. σ−1

(11)

Equation (11) has a simple interpretation: because shops have identical costs and the traveler’s utility is symmetric with respect to the varieties of goods, the price is the same for all shops and is increasing in the marginal cost. Moreover, p decreases and approaches the marginal cost as σ increases, i.e. monopolistic competition hits harder on shops’ margins as the elasticity of substitution between their products grows larger, driving prices down to the competitive level. Clearly, a shop profit is the same across shops and, given the optimal price and the transfers sF ≥ 0 and sL ≥ 0, is π=

K I˜ − sJ DJ + zJ , ΠM

13

(12)

where K ≡ σ −1 P 1 + P τ −1




τ 1−τ

.

(13)

Notice that K, together with P and Π, incorporates all the exponential functions and allow us to represent equilibrium values with simpler expressions. We summarize the subgame equilibrium play in the consumer goods market in the following lemma. Lemma 1. Assume that: (i) condition (7) is satisfied; (ii) 0 <

TL 1−Π

< TF < 1; and (iii) the contract

(sJ , zJ ) with carrier J is agreed to by the Mall. Then: • Consumers with income below

TL 1−Π

do not fly; those with income between

TL 1−Π

and TF fly with the

Low Cost airline; and those with income above TF fly with the Full Service carrier. • Destination shops charge the same price, p =

σ σ−1 c,

and each shop profit is (12).

k = I ; • Non-traveling consumers spend all their income on the num´eraire and their utility is UN k

passenger k flying with airline J purchases the quantity q0k = the quantity qik =

q0k

σ

P τ M σ−1

Ik −TJ 1+P 1−τ

of the num´eraire good and

of all other goods i = 1, ..., M . The utility of travelers is (5).

Two-sidedness. We have characterized the optimal decisions of travelers and shops, given carriers strategies. The analysis has been standard up to this point. However, before studying airlines’ decisions, we shall notice that our model has a distinct two-sided framework. Indeed, airlines in our model are platforms connecting consumers on one side to shops on the other. A common definition of two-sided markets — see Rochet and Tirole (2006) — is that, cœteris paribus, the net utility of players on one side increases with the number of players on the other.27 In our setting, this amounts to saying that a traveler’s utility increases with the number of shops at the destination, M , and a shop profit increases with the number of travelers arriving at the destination. To show that our model is indeed a two-sided market, notice that the number of consumers arriving at the destination is 1 − λ with λ ≡

TL 1−Π .

Thus, the market we are modeling can be defined a two-sided

market if a traveler’s utility (5) increases with M and a shop profit (12) gross of the payments to and from the carrier(s) decreases with λ. Substituting optimal price (11) into (5) yields utility for a traveler k who flies — i.e., with income Ik ≥

TL 1−Π

— equal to

UJk = QJ + (Ik − TJ ) 1 + M

τ −1 σ−1



σ−1 cσ

1 τ −1 ! τ −1

∀ J = L, F

(14)

27 Another definition — see, again, Rochet and Tirole (2006) — is that the volume of transactions depends on how the total price paid to the platform is shared between sides. Here it is clearly so: suppose that carrier J deals with the Mall and charges airfare TJ to travelers and SJ per traveler to the Mall — i.e., a total platform price of TJ + SJ . It is clear from (9) and Figure 1 that the volume of transactions I˜ as well as the overall flight demand 1 − TL /(1 − Π) are affected by a change to the composition of the total platform price, either directly (under Low Cost – Mall contracting) or through strategic interaction (under Full Service – Mall contracting).

14

and profit for any shop equal to π=

K I˜λ . ΠM

(15)

where I˜λ is the aggregate net income (9) rewritten as a function of λ, that is I˜λ ≡

Z

1

Z

TF

(Ik − TF ) dIk + TF

(Ik − TL ) dIk . λ

It is easy to see that a traveler’s utility increases with M , while a shop profit increases as the number of travelers increases — i.e., λ decreases. We summarize the previous discussion in the next proposition. Proposition 1. The flight market is characterized by network externalities typical of a two-sided market. In particular, take any profile of airfares TJ , qualities QJ and transfers sJ and zJ , J = L, F , such that some consumers travel and shops agree to contracts. Then, travelers gain from a larger number of shops at the destination, M , and shops profit from a larger number of travelers, 1 − λ. We have shown that, in fact, airlines in our model are platforms of a two-sided market where the sides to be connected are travelers/consumers and destination shops. In fact, on the one hand, travelers benefit from a larger number of shops at the destination due to the love for variety embedded in their Dixit and Stiglitz (1977) utility function. On the other hand, shops clearly profit from a larger number of clients arriving at the destination. Notice, however, that (i) consumers are connected to the same shops regardless of the carrier they travel with, that is, the destination’s set of shops is not a strategic variable; (ii) carriers compete on airfares, TJ , and flight quality, QJ , and, in particular, the flight quality enters the utility of travelers independent of destination consumption in our setup. Hence, carriers are not pure platforms whose value to a consumer is mainly determined by the network externality they generate. As we will show, this allows us to characterize an equilibrium with vertical differentiation in which the intrinsic value of the flight plays a distinct role, neatly distinguishing our model from those of Argenziano (2008) and Gabszewicz and Wauthy (2014). In the next section we will develop the analysis of airlines’ pricing strategies and characterize optimal contracts between the airlines and the Mall.28 Let’s thus denote the Mall profit when it strikes a contract with carrier J as πS =

K˜ I − SJ DJ + ZJ , Π

where the subscript S denotes the Mall. Note that

K Π

represents the share of travelers’ net income spent

at the destination given the equilibrium on the destination retail market. Consistently, it takes values between zero and one as proved by the following lemma. Lemma 2. For all admissible values of the relevant parameters, i) 0 < K < Π < 1, and ii) Π < P . 28

While shops optimization was clearly done at the shop-level, as shops are identical it is theoretically plain to assume that they coordinate perfectly when dealing with airlines. Hence, we shift the focus of our analysis from the single shop to the collective entity.

15

The ordering between P , Π and K stated in Lemma 2 is very useful to characterize equilibria as it allows us to rank airfares, profits, etc. as well as to perform comparative statics.

4

Market Structures

We are interested in studying the viability of commercial agreements between airlines and destination businesses. We will then characterize the optimal contracts proposed by different carriers to the Mall and show how our model closely reproduces the special real world contracts typical of the air travel industry. Notice, however, that any contract must satisfy the Mall participation constraint. Namely, the Mall has the possibility to implement standard competition between the carriers by refusing to sign any cooperation agreement. This determines the reservation profit of the Mall. Hence, in what follows we characterize first the standard competition benchmark. We will then characterize the subgames in which the Mall signs an agreement with either company and, lastly, compare the outcomes of these three market structures. As discussed in Section 5, we focus on exclusive dealing and do not analyze the grand-coalition contract between the Mall and both carriers.

4.1

Standard Competition Benchmark

Let the benchmark competition scenario, in which no contract is signed between the Mall and any carrier, be denoted by a superscript C. Profits of the Low Cost, Full Service and Mall are πiC , i ∈ {L, F, S}. Optimal airfares are chosen simultaneously to maximize πLC = TL DL

and

πFC = TF DF ,

yielding TLC =

1−Π 4

and

TFC = 21 .


Notice that TLC , TFC is an equilibrium only if (7) is satisfied — i.e., QF ≥ QC F,

with

QC F ≡

1+Π 4Π .

(Assumption 1)

Finally, equilibrium profits in the competition benchmark are all positive and πLC is decreasing in Π (see Table 1 in the Appendix). This is because flying with the Low Cost airline, which has zero quality, increases travelers’ utility only by allowing them to purchase destination goods. In fact, as Π increases and destination goods become more expensive, the carrier reduces its fare to avoid losing travelers, and the final effect is a net loss to the airline. We summarize the above in the following proposition. Proposition 2. Assume that Mall–carriers contracting is not possible and that Assumption 1 holds. Then, the air travel industry equilibrium exists and is characterized by airfares TLC = 16

1−Π 4

and TFC = 12 .

The quality provided by the Full Service carrier cannot be lower than QC F ≡

1+Π 4Π .

Equilibrium profits are

given in Table 1 in the Appendix. Equilibrium demand for flights and goods are those of Lemma 1. We close this subsection by noting that any agreement between an airline and the Mall, which we will analyze next, must be Pareto improving on the standard competition outcome for the parties.

4.2

Low Cost – Mall Agreement

Equipped with the benchmark case, we now characterize optimal airfares TF and TL and transfers SL and ZL when the Low Cost airline is the carrier that cooperates with the Mall under exclusivity. Denoted by a superscript L the case at hand, the Low Cost carrier sets TLL to jointly maximize its own profits and those of the Mall, i.e., π L = πSL + πLL . It will then extract all the possible surplus from the Mall
through the two-part tariff SLL , ZLL where SLL is the per-passenger transfer while ZLL is the fixed part. The airlines choose simultaneously TLL and TFL to maximize, respectively, πL =

K˜ ΠI +

TL DL

and

πFL = TF DF ,

where SLL and ZLL wash out of profits π L as they are mere transfers between the carrier and the Mall. Optimal fares are TLL =

(1−Π)2 (Π−K) 2(Π+(1−2Π)(Π−K))

and

TFL = 12 .

Using Lemma 2, it is easy to show that TLL < TFL . Assuming for a moment that (7) is satisfied, let’s move backward and characterize the optimal choice of SLL . Following standard implementation theory, SLL is set to implement the airfare TLL that maximizes joint profits as an endogenous choice of the Low Cost carrier — i.e., SLL solves ∂



(TL +SLL )

  TL TFL − 1−Π

∂TL



= 0,

which yields:

SLL =

K(1−Π) 2(Π+(1−2Π)(Π−K)) .

TL =TLL


Finally, TLL , TFL , SLL are equilibrium strategies only if (7) is satisfied, i.e., QF ≥ QL F,

with

QL F ≡

1−Π(Π−K) 2(Π+(1−2Π)(Π−K)) .

(Assumption 2)

C Notice that, again by Lemma 2, QL F > QF : it is now more difficult to induce travelers to choose a full

service flight. In fact, due to the subsidy SLL paid by the Mall to the Low Cost carrier, the latter can reduce its airfare (TLL < TLC ), thereby inducing a stronger preference for low cost flights, which has to be compensated with higher flight quality from the Full Service airline. Before characterizing the optimal fixed transfer ZLL , let’s consider the profits net of the fixed part of the two-part tariff. These are reported in Table 1. Given Lemma 2, it is not difficult to show that πLL > πLC and πFC = πFL for all values of the price indexes — i.e., the Low Cost-Mall agreement is beneficial to the Low Cost carrier while it leaves the Full Service carrier indifferent vis-` a-vis the 17

competition benchmark. While the former result is intuitive insofar as cooperation gives the Low Cost carrier one more instrument, SLL , the latter depends on the fact that the Full Service carrier demand is only determined by a cash constraint, which, in turn, is not affected by the agreement between the Low Cost airline and the Mall. Furthermore, the zero cost of quality assumption implies that the higher C quality provided by the Full Service (QL F > QF ) has no impact on its profits. If we assumed a cost for

quality, then the natural result (πFC > πFL ) would be obtained. As for the Mall profits, it can be shown that πSL > πSC if and only if Π > 5/6: in other words, given the transfer required by the airline, the Mall profits are larger under cooperation when the prices charged at the destination are large enough.29 We can now complete the characterization of the optimal agreement between the Low Cost airline and the Mall. The fixed part of the contract is clearly ZLL = πSC − πSL : it amounts to a transfer from the airline to the Mall when the global price index falls short of 5/6 while it is a payment from the Mall to the carrier otherwise. The intuition is simple: when prices are high the subsidy SLL is more than covered by travelers’ purchases and the Mall generates an additional surplus vis-` a-vis the competition benchmark, which is appropriated by the Low Cost airline. When, instead, prices are low, after paying the per-passenger subsidy, the Mall is worse-off than at the standard competition scenario and the airline has to compensate it with a transfer ZLL > 0. We have then established the following proposition. Proposition 3. Assume exclusive dealing between the Mall and the Low Cost airline (SFL = ZFL = 0) and assume Assumption 2 holds. Then, the air travel industry equilibrium exists and is characterized by airfares TLL =

(1−Π)2 (Π−K) 2(Π+(1−2Π)(Π−K))

and

TFL = 12 .

The quality provided by the Full Service carrier cannot be lower than QL F ≡

1−Π(Π−K) 2(Π+(1−2Π)(Π−K)) .

The contract between the Low Cost carrier and the Mall prescribes the per-passenger transfer SLL =

K(1−Π) 2(Π+(1−2Π)(Π−K))

and the fixed transfer ZLL = πSC − πSL that is positive if, and only if, Π < 5/6. Equilibrium profits (net of the fixed transfers) are in Table 1 in the Appendix. Demand for flights and goods are those of Lemma 1.

4.3

Full Service – Mall Agreement

We now turn to the case of the Full Service airline cooperating with the Mall. In this case, adopting
a similar notation, we characterize the optimal exclusive contract SFF , ZFF proposed by a Full Service 29

More precisely, Π > 5/6 if and only if P > 5 6τ −1 − 5τ −1




18

1 1−τ

1

, with P = M 1−σ

σ c σ−1

in equilibrium.

carrier who maximizes joint profits π F = πSF + πFF . Profits at the stage of setting airfares are  πLF = TL TF −

TL 1−Π



πF =

and

K˜ ΠI +

TF (1 − TF ) .

The optimal fares are Π−K TLF = (1 − Π) 3(Π−K)+Π(1−K)

and

Π−K TFF = 2 3(Π−K)+Π(1−K) ,

which, again by Lemma 2, are correctly ranked and properly define the demand function of Figure 1. The optimal subsidy SFF is obtained as before and equals SFF =

K(1−Π) 3(Π−K)+Π(1−K) .

Finally, there is demand for Full Service flights only if (7) is satisfied, i.e., QF ≥ QFF ,

with

QFF ≡

Π−K 1+Π Π 3(Π−K)+Π(1−K) .

(Assumption 3)

It is worth noticing that QFF < QC F : it is easier for the Full Service carrier to attract travelers when it cooperates with the Mall than under standard competition. In fact, because of the Mall subsidy SFF , the Full Service airline can reduce its airfare (TFF < TFC ) and this reduction is proportionally larger than the strategic reduction in flight fare of the Low Cost airline (TLF < TLC ), inducing travelers to prefer a full service airline at lower quality levels. Profits are reported in Table 1 in the Appendix. Using Lemma 2 it can be easily shown that πFF > πFC , πLF < πLC and πSF < πSC for all values of the price indexes, or, in words, cooperation with the Mall benefits the Full Service carrier and damages both the Low Cost carrier and the Mall relative to the competition scenario. The first inequality is, again, quite intuitive as the Full Service carrier has an additional competitive instrument. The second hinges on the fact that now the reduced Full Service carrier fare erodes the demand of the Low Cost airline, downsizing equilibrium profits. Finally, the Mall profits, if not compensated by a fixed transfer, are lower than under competition regardless of the level of Π. We can now complete the characterization of the optimal agreement between the Full Service airline and the Mall. The fixed part of the contract is clearly Z F = πSC − πSF and amounts to a transfer from the airline to the Mall. We have thus established the next proposition. Proposition 4. Assume exclusive dealing between the Mall and the Full Service carrier (SLF = ZLF = 0) and assume Assumption 3 holds. Then, the air travel industry equilibrium exists and is characterized by airfares Π−K TLF = (1 − Π) 3(Π−K)+Π(1−K)

and

Π−K TFF = 2 3(Π−K)+Π(1−K) ,

and by a minimum quality level QFF ≡

1+Π Π−K Π 3(Π−K)+Π(1−K) .

19

The contract between the Full Service carrier and the Mall prescribes the per-passenger transfer SFF =

K(1−Π) 3(Π−K)+Π(1−K)

and the fixed transfer ZFF = πSC − πSF . Equilibrium profits (net of the fixed transfers) are given in Table 1. Demand for flights and goods are those of Lemma 1.

4.4

Comparing Market Structures

We now compare the market structures characterized above along several dimensions. The next corollary summarizes results discussed in Sections 4.2 and 4.3. Corollary 1. For all admissible values of c, ρ, ϕ and M the following inequalities hold: TLC > TLF > TLL ,

TFC = TFL > TFF ,

C F QL F > QF > QF ,

πLL > πLC > πLF ,

πFF > πFC = πFL .

Most intuitions behind Corollary 1 were discussed above. We remark here that the airfares of both carriers are highest in the benchmark scenario, when no agreements are signed. In fact, when a carrier strikes a deal with the Mall, the latter subsidizes the former so as to allow the carrier to charge lower airfares and embark a larger number of potential customers. Without a deal with the Mall, the carrier does not internalize this ‘platform externality’ and charges higher airfares that discourage consumers from traveling. This has neat implications for the flight demand — i.e., the number of travelers — as detailed in the next corollary. Corollary 2. For all admissible values of c, ρ, ϕ and M the following inequalities hold: i DFi > DL

i ∈ {C, L, F } ;

DFF > DFC = DFL ;

L C F DL > DL > DL ;

L F C DL + DFL > DL + DFF > DL + DFC .

The first inequality confirms a standard vertical differentiation result: the quality leader enjoys a larger market share. And this is true regardless of the market structure. The second and third inequalities confirm the basic intuition that cooperation with the Mall allows a carrier to reduce fares and thereby increase his market share of flights. The last inequality states that overall flight demand increases when a carrier deals with the Mall and is maximized when it is the Low Cost carrier to do so. Finally, we briefly comment on the assumption that travelers purchase with certainty from destination shops regardless of the carrier they fly with and discuss its consequences on our results. As mentioned in the introduction, the realistic assumption suggested by casual empiricism would be that i) passengers make purchases at the destination only with some probability; ii) carriers actively patronize destination businesses through ad hoc adverts to induce passengers to make purchases; and iii) low-income consumers are more sensitive to these advertising strategies. If this were the case, a low cost carrier would be more effective in generating network externalities. In fact, by i) and iii) it could direct passengers to shops more efficiently. Hence, the results of Corollaries 1 and 2 would hold even more strongly. 20

5

Endogenous Market Structure

In Section 4 we have characterized the equilibrium of the flights industry taking the market structure as given. We now relax this assumption allowing the market structure to be determined endogenously. In particular, we assume that contracts between an airline and the Mall are signed under exclusivity. This assumption is natural on two grounds: first, under non-exclusivity carriers would form a cartel to maximize the grand coalition profits, triggering the intervention of antitrust authorities; second, the type of contracts Ryanair has on its bases is never stipulated between a local stakeholder and more than one carrier. Under the exclusivity assumption, the Mall chooses which contract to accept, if any, among the two offered by the airlines. We wish to understand which market structure emerges in equilibrium among those characterized in Section 4, and how this depends on the relevant parameters of the model. Propositions 3 and 4 have proved that cooperation with either airline always increases the joint profits of the cooperating parties vis-` a-vis the standard competition scenario. Hence, in the endogenous equilibrium market structure the Mall certainly cooperates with a carrier. To understand which airline will strike a contract with the Mall, suppose the Mall accepts the offer of the Low Cost carrier — to be better specified later. Then, the Full Service airline earns πFL in equilibrium. However, if it cooperated with the Mall, they would jointly earn π F . Hence, the best counteroffer the Full Service is willing to make to the Mall guarantees the Mall at most π F − πFL . As a consequence, the contract offered by the Low Cost carrier has to let the Mall earn at least this much. Finally, the Low Cost carrier makes an offer to the Mall if, and only if, it eventually earns more dealing with the Mall rather
than letting the Full Service contract with the Mall and earning πLF — i.e., π L − π F − πFL > πLF . Using a symmetric argument, it is easy to find an analogous condition for the emergence of a contract between
the Full Service airline and the Mall as the endogenous market outcome — i.e., π F − π L − πLF > πFL . We conclude that the endogenous market structure features Low Cost-Mall contracting if, and only if, π L − πLF > π F − πFL .

(16)

It turns out that, under any set of feasible parameters, condition (16) strictly holds, as stated in the following proposition. Proposition 5. Assume that cooperation contracts between the Mall and airlines are exclusive. Then, the optimal market structure of the airline industry always features cooperation between the Low Cost carrier and the Mall. The variable part of the contract as well as the equilibrium airfares of the airlines are those characterized in Proposition 3 while the fixed part is ZLE = π F − πFL − πSL . Proposition 5 simply states that Low Cost-Mall dealing generates higher total profits than Full Service-Mall dealing does. In fact, condition (16) can be rewritten as πLL + πSL + πFL > πLF + πSF + πFF , 21

The inequality above implies that cooperation with the Low Cost carrier is relatively more efficient in generating extra revenues vis-` a-vis the benchmark competition scenario. In fact, the expansion of the total number of travelers due to the reduction of

TL 1−Π

(the extensive margin) is a direct effect when the

Mall deals with the Low Cost while it is an indirect one when the Mall deals with the Full Service airline. In this case the Low Cost carrier reduces its airfare and expands the market only as a strategic response to the lower Full Service airfare. Before turning to welfare analysis, we note that the result in Proposition 5 would be strengthened if we incorporated operational (variable) costs into the model. In fact, in a vertically differentiated model a low cost carrier naturally sustains lower costs per passenger than a full service one. This translates into more efficiency when it comes to exploiting the extensive as well as the intensive margins at the ˜ is airfare setting stage. As a consequence, the shopping income available for destination purchases (I) relatively larger when a low cost carrier deals with the Mall, as opposed to a full service one. Hence, dealing with a low cost carrier allows the Mall to better exploit the network externalities generated by air travel.

5.1

Welfare

We now evaluate the welfare effects of the agreement reached by the Low Cost carrier and the Mall. We want to understand whether Low Cost-Mall contracting improves welfare for the consumers and for the economy as a whole relative to the competition scenario of Section 4.1. k = I for non The consumers’ welfare is measured by the indirect utility function, which equals UN k

travelers and it is reported in (5) for those who travel. Profits are those of Sections 4.1 and 4.2. We assume that the domestic market is competitive so that we can ignore the home good producer surplus throughout the analysis. Consider first the consumers’ utility in equilibrium, i.e. the consumer welfare, CW . It is Z

1

CW = TF

  Z Ik − TF QF + dIk + Π

TF TL 1−Π



Ik − TL Π



Z dIk +

TL 1−Π

Ik dIk

(17)

0

Assuming that QF is given and (7) is satisfied in both scenarios, and recalling that, by Corollary 1, the Full Service carrier charges the same airfare in both scenarios (TFC = TFL = 21 ), it is immediate to see that the first term of (17) is constant across scenarios. Next, since TLL < TLC , the second term is larger under Low Cost-Mall contracting than under the competitive scenario for two reasons. On the one hand, travelers are left with more income for shopping, on the other hand, more consumers with relatively lower income can travel. Finally, the third term is smaller under Low Cost-Mall contracting because less consumers stay at home. The net effect is necessarily positive as those consumers who switch from staying at home to traveling are clearly better-off in equilibrium. Hence, consumer welfare CW is larger under Low Cost-Mall contracting than under competition. We now turn to the airline industry and destination shopping sector. We shall compare overall 22

profits under competition, πLC + πSC + πFC , to those obtained by shops and carriers under Low Cost-Mall contracting, πLL + πSL + πFL . Given TFC = TFL = depends on its airfare, so that

DFC

=

DFL ,

1 2

and because the Full Service carrier demand only

its profits are the same under both scenarios, that is πFC = πFL

— see Table 1. As to the comparison between πLL + πSL and πLC + πSC , the former obviously exceeds the latter because, were it the opposite, no contract could be agreed on between the Mall and the Low Cost carrier. Hence, the joint profits of the carrier and the Mall are larger when the Low Cost carrier cooperates with the Mall vis-` a-vis the standard competition scenario. We summarize this in the next proposition. Proposition 6. Assume that the home good sector is competitive. Then, both the consumer welfare and the sum of the profits of the carriers and the Mall are higher under Low Cost-Mall contracting than under standard competition.

5.2

When Dealing with the Mall is a Good Business

We close the paper by highlighting a key feature that, we believe, is at the heart of the success of the business model of Ryanair. In particular, we try to answer the natural question about the key factor determining the profitability of carriers when dealing with local stakeholders. In fact, while our model predicts that the unique outcome of the industry game features Low Cost-Mall contracting, in reality many routes are operated in the absence of any such contract, thus resembling our competition scenario. To rationalize the absence of Low Cost-Mall contracting in some real instances, it is enough to assume that there exists a fixed cost of operating a specific route through a carrier-stakeholders contract. Under this natural assumption, only routes that guarantee enough profits will be operated under the ultra low cost business model. We thus focus on those factors that magnify the network externality within our model. In particular, we notice that the shopping motive of travelers — the main driver of the model — is stronger when home and destination goods are poor substitutes. Hence, we expect that the value generated by Low Cost-Mall cooperation and the profits of the Low Cost carrier, are larger when ϕ is small — or, which is the same, when the elasticity of substitution, τ , is close to its lower bound which equals one. In fact, when ϕ is small, home and destination goods are poor substitutes and travelers like consuming both. Hence, the global price index, Π, which is the cost of a unit of utility from goods consumption, is lower the smaller is ϕ. Hence, it can be shown that the share of net income spent by travelers at the destination,

K Π,

is larger the less substitutes are home and destination goods, provided that M ≥ 3.

This in turn allows the Low Cost carrier to make larger profits by reaping part of the income spent at the destination via the contract with the Mall. Hence, if we let the profit of the Low Cost carrier when
the market structure is endogenous and it deals with the Mall be denoted by πLE = π L − π F − πFL , we expect that πLE is larger the less substitutes are home and destination goods (small ϕ). To check that our intuition is correct, we would differentiate the Low Cost carrier profit with respect

23

0.06 0.04 0.02 0.00 0

1

ρ

ϕ

0

1

Figure 2: πLE when c = 1 and M = 3 to ϕ and sign the resulting expression. However, the profit πLE is a complicated exponential function of c, M , ρ and ϕ and is not even computer-solvable. We then simulate the carrier profit and plot πLE as a function of ρ and ϕ for given levels of c and M . Figure 2 illustrates the Low Cost carrier profit when dealing with the Mall when c is normalized to 1 and M = 3.30 The shape of the surface confirms our intuition: the less home and domestic goods are substitutes, the higher the profits of the Low Cost carrier from dealing with the Mall.

6

Discussion: beyond Ryanair

Before concluding, we broaden the perspective of our analysis and briefly discuss its managerial insights in connection with two important theories of the received management literature. Several management authors (see Adner (2002), Govindarajan and Kopalle (2006), Markides (2006) and Yu and Hang (2010) among others) argue that low cost carriers are “Disruptive Innovators”, in line with the theory developend by Bower and Christensen (1995). A low cost carrier enters the market with organizational innovations providing the basic transportation service at much cheaper fares, albeit at a lower quality level. Using this strategy — also referred to as “new-market disruptive innovation” from Christensen and Raynor (2003) — a low cost carrier is able to serve a segment previously excluded by the air-travel market. Subsequently, the disruptive innovator learns to provide higher quality (comparable to that of the incumbents) keeping the costs low, thereby stealing their customers and disrupting their business. The first phase of the disruptive innovation strategy — i.e., entry by creating a new market for 30

As a robustness check, in the Appendix we show the same graph for different values of c and M .

24

previously unserved travelers — fits the low cost business model well, and those of Southwest and Ryanair in particular. As to the second phase, some low cost carriers have recently tried to raise the quality of their service — e.g., by launching (sort of) business-class fares and becoming more hybrid carriers. However, we notice that: i) it is unclear whether they intend to disrupt conventional incumbents or, rather, to differentiate from other low cost carriers; ii) it seems that the costs of some quality characteristics (e.g. leg space, luggage allowances, etc.) cannot be compressed to the point of fully disrupting conventional carriers business model; iii) more importantly, it is unclear that this is an economically sound strategy: as documented by Alamdari and Fagan (2005), it seems that going hybrid is a less profitable strategy than sticking to the ‘original low cost model’. Regardless of whether disruptive innovation really explains the advent of low cost carriers, we take a broader perspective to rationalize the unique strategy of a ultra-low cost carrier such as Ryanair. In particular, we think that the special feature of the strategy of Ryanair is to exploit two-sided pricing to push down airfares up to the point of attracting a substantial amount of latent demand previously not served by established carriers. This strategy goes beyond the cost-saving typical of low cost flights and mainly aims at enlarging the pie rather than eating a larger slice of it. It seems to us that the concept of “Blue Ocean Strategy” (Kim and Mauborgne (2004)) better fits the underlying logic. According to this, Ryanair has created an “uncontested market space” in order to avoid tough competition with established carriers. In this case the uncontested market space is created by reducing prices so to make traveling possible to a large share of low-to-mid income consumers for whom traditional flights were not affordable. According to this view Ryanair does not primarily aim at stealing customers from established carriers. It rather exploits the latent demand of potential travelers not adequately served by incumbents. And, taking a wider view of the market than traditional airlines, it does so by exploiting the network externalities generated by its core business of moving people across markets. The Blue Ocean Strategy enacted by Ryanair is, to the best of our knowledge, an unicum in the airline industry. It seems that no competitor has been able to follow its lead. Perhaps this is because this strategy requires, on the one hand, building the capability to deal with dispersed and diverse stakeholders and, on the other hand, a quite bold stance given the risk of being sued for state aid by EU authorities when dealing with local public entities. Nonetheless, the analysis we perform on Ryanair has a broader validity that extends beyond the airline industry. In particular, the main intuitions derived by our model apply to any industry in which: i) there is some element of (vertical) differentiation in a primary market and consumers value quality; ii) sellers provide a service which generates positive network externalities to third parties; iii) the innovating firm serves the market segment which generates the largest externalities; iv) the pricing of these externalities allows the innovator to cross-subsidize its customers, thereby reducing prices and expanding demand via the extensive margin in the primary market. To clarify how our analysis can shed light on cases different from Ryanair, we briefly expand on a

25

particularly interesting one: Metro free press.31 Metro is an arguably low quality32 daily newspaper that is delivered for free as opposed to established outlets that are commonly sold in kiosks or via subscriptions. Owing to its free policy, Metro reaches an extremely large number of readers, most of whom would not buy traditional newspapers. The industry is therefore vertically differentiated and the low cost seller plays on the extensive margin reducing the price (down to zero in this case) to earn readers who would otherwise not read a printed outlet. As it turns out, Metro can afford free daily delivery of so many copies precisely by exploiting the platform nature typical of news outlets more heavily than others do. In fact, compared to traditional newspapers that rely on advertising to finance themselves only to some extent, Metro hosts (a lot) more commercials on its pages and is entirely financed through ads. Hence, while the contracts between advertisers and news outlets may not be exclusive as in our framework, the logic behind the strategy and the positioning of Metro in the markets for readers and advertisers is the one at the heart of our analysis.33

7

Conclusion

We have developed a simple model of the air travel industry that rationalizes the extremely low airfares practiced by the (ultra) low cost carrier Ryanair. Our model recognizes that Ryanair exploits the twosided nature of air traveling: bringing potential buyers closer to potential sellers. Pricing both sides of the market rather than focusing just on cost-containment and quality competition — as standard low cost carriers in regular vertically differentiated markets — Ryanair has been able to further reduce the cost of flying to potential travelers inducing higher demand and allowing lower income people to travel, thereby implementing a classical blue ocean strategy. We showed that under exclusivity two-sided pricing is adopted by low cost no-frills carriers rather than established high quality airlines, because the low cost carrier can naturally and more efficiently exploit the extensive margin. Finally, our model predicts that two-sided pricing is more profitable the less destination and home goods are substitutes in travelers’ preferences, as this magnifies network externalities. This suggests that when travelers are likely to find goods and services at the destination that are difficult to find at home, such as specific touristic attractions, we should expect to see more often these types of contracts between Ryanair and destination stakeholders. The findings of our model correspond to facts that have been observed in practice. Moreover, our work provides an analytic framework that can be used to understand a wider set of industries and cases beyond Ryanair.

31

See www.readmetro.com. See also the case study Khanna, Oberholzer-Gee, Dessain, Jensen, and Sjoman (2007). It is a daily outlet designed for a 20-minute read — i.e., for urban commuters — with no in-depth analyses, inquiries, opinions, editorials, etc. It is filled with ads and features very simple graphic design. It is delivered in 74 local editions in 124 urban areas of 22 countries in 13 languages. 33 We notice here that two-sided pricing is standard in media markets, as extensively documented by the literature on two-sided markets. Metro enacted a Blue Ocean Strategy by lowering quality and pushing to zero the price charged to readers. The current outcome in both cases, Metro and Ryanair, is similar. However, the industrial dynamics were different. In fact, Ryanair innovated more radically since it introduced two-sided pricing into the flight industry for the first time. 32

26

References Adner, R. (2002): “When are Technologies Disruptive? A Demand-Based View of the Emergence of Competition,” Strategic Management Journal, 23, 667–688. Alamdari, F., and S. Fagan (2005): “Impact of the Adherence to the Original Low-cost Model on the Profitability of Low-cost Airlines,” Transport Reviews, 25(3), 377–392. Alderighi, M., M. Nicolini, and C. A. Piga (2015): “Combined effects of capacity and time on fares: insights from the yield management of a low-cost airline,” The Review of Economics and Statistics, 97(4), 900–915. Argenziano, R. (2008): “Differentiated Networks: Equilibrium and Efficiency,” The RAND Journal of Economics, 39(3), 747–769. Armstrong, M. (2006): “Competition in two-sided markets,” The RAND Journal of Economics, 37(3), 668–691. Bower, J. L., and C. M. Christensen (1995): “Disruptive Technologies: Catching the Wave,” Harvard Business Review, pp. 43–53. Christensen, C. M., and M. E. Raynor (2003): The Innovator’s Solution: Creating and Sustaining Successful Growth. Harvard Business School Press. Dixit, A. K., and J. E. Stiglitz (1977): “Monopolistic Competition and Optimum Product Diversity,” American Economic Review, 67(3), 297–308. Doganis, R. (2006): The Airline Business. Routledge. Flores-Fillol, R., A. Iozzi, and T. Valletti (2015): “Platform pricing and consumer foresight: the case of airports,” mimeo. Franke, M. (2004): “Competition between network carriers and low-cost carriers: retreat battle or breakthrough to a new level of efficiency?,” Journal of Air Transport Management, 10(1), 15–21. Gabszewicz, J. J., and X. Y. Wauthy (2014): “Vertical product differentiation and two-sided markets,” Economic Letters, 123, 58–61. Govindarajan, V., and P. K. Kopalle (2006): “The Usefulness of Measuring Disruptiveness of Innovations Ex Post in Making Ex Ante Predictions,” The Journal of Product Innovation Management, 23, 12–18. Ivaldi, M., S. Sokullu, and T. Toru (2015): “Airport prices in a two-sided market setting: major US airports,” mimeo. Khanna, T., F. Oberholzer-Gee, V. Dessain, A. D. Jensen, and A. Sjoman (2007): “Metro International S.A.,” Harvard Business Review, Case Study 708-429. Kim, W. C., and R. Mauborgne (2004): “Blue Ocean Strategy,” Harvard Business Review.

27

Malighetti, P., S. Paleari, and R. Redondi (2009): “Pricing strategies of low-cost airlines: The Ryanair case study,” Journal of Air Transport Management, 15, 195–203. Markides, C. (2006): “Disruptive Innovation: In Need of Better Theory,” The Journal of Product Innovation Management, 23, 19–25. Ribeiro, V. M., J. Correia-da-Silva, and J. Resende (2014): “Nesting vertical and horizontal differentiation in two-sided markets,” CEF working paper. Rochet, J.-C., and J. Tirole (2006): “Two-sided markets: a progress report,” The RAND Journal of Economics, 37(3), 645–667. Tirole, J. (1988): The Theory of Industrial Organization, vol. 1 of MIT Press Books. The MIT Press. Yu, D., and C. C. Hang (2010): “A Reflective Review of Disruptive Innovation Theory,” International Journal of Management Reviews, 12, 435–452. Zhang, A., and A. Czerny (2012): “Airports and airlines economics and policy: an interpretive review of recent research,” Economics of Transportation, 1, 15–34.

28

Appendix Proof of Lemma 1: it is useful to start from the consumer’s optimal behavior (third point). Clearly, a consumer who stays at home spends all his income in the num´eraire. He purchases a quantity q0k = Ik k = I . Suppose instead a consumer travels with airline J. of the home good and his utility is clearly UN k Then, his constrained optimization is represented by the Lagrangian  L (q0k , q1k , ..., qM k , λ) = QJ +

q ϕ 0k

M X

+

! ϕρ  ϕ1

  XM  + λ Ik − q0k − TI − pi qik .

ρ qik

i=1

i=1

Taking the first order conditions with respect to q0k and to qjk , j = 1, ..., M , one obtains, respectively 

M X

q ϕ + 0k

! ϕρ  1−ϕ ϕ ρ qik



ϕ−1 = λ, q0k

(A1)

ρ−1 = λpj . qjk

(A2)

i=1

 q ϕ + 0k

M X

!  1−ϕ ϕ ϕ ρ

ρ qik

M X



i=1

! ϕ−ρ ρ ρ qik

i=1

Using the FOCs on qik and qjk , i, j ∈ {1, ..., M }, i 6= j, we obtain the usual price ratio result qik = qjk from which, using qik =

  pj pi

1 1−ρ



pj pi



1 1−ρ

,

qjk , we obtain M X

ρ

ρ ρ qik = pj1−ρ qjk

M X

ρ

piρ−1 ,

i=1

i=1

and, substituting into (A2),  q ϕ 0k

ϕ 1−ρ

+ pj

ϕ qjk

M X

ρ ρ−1

! ϕρ  1−ϕ ϕ

pi



ϕ−ρ 1−ρ

pj

ϕ−ρ qjk

i=1

M X

ρ ρ−1

pi

! ϕ−ρ ρ ρ−1 qjk = λpj

i=1

which, using λ from (A1) and simplifying, yields 1 ρ−1

qjk = pj

q0k

M X i=1

29

ρ ρ−1

pi

ϕ−ρ ! ρ(1−ϕ)

.

(A3)

Let’s now use the budget constraint to solve for the numeraire q0k q0k = Ik − TJ −

XM i=1

pi qik

which, using (A3), simplifies to Ik − TJ  ϕ(1−ρ) .  ρ ρ(1−ϕ) PM ρ−1 1+ i=1 pi

q0k =

(A4)

Finally, let’s plug (A4) into (A3) to solve for qjk qjk = 1 1−ρ

pj

 PM

ρ ρ−1



Ik − TJ 

ρ−ϕ ρ(1−ϕ)

i=1 pi

1 +

 PM

ρ ρ−1

i=1 pi

 ϕ(1−ρ)

.

(A5)

ρ(1−ϕ)



To make the Marhallian demand function just derived readable, define the destination price index as

P ≡

M X

ρ ρ−1

pi

! ρ−1 ρ .

(A6)

i=1 1 1 Using (A6) and the relations σ = 1−ρ and τ = 1−ϕ , the Marshallian demand for the numeraire and the goods of the Mall can thus be written as (3) and (4) respectively. The indirect utility function of traveler k, (5), is easily obtained by plugging the Marshallian demand functions into the utility of traveler k and defining the global price index as
1 Π = 1 + P 1−τ 1−τ . (A7)

The proof of the second point is done in the text preceding Lemma 1 and omitted here. The first point of the lemma is proved as follows. First, a necessary and sufficient condition for the existence of a demand for traveling is that (6) holds for some income level. Second, a positive demand for the Full Service carrier exists if condition (7) is satisfied and the airfare TF is affordable to some consumer, i.e. TF < 1. We assume (7) holds and we note that it is independent of individual income, meaning that a consumer who can afford to fly with the Full Service carrier will always prefer to do so rather than traveling with the Low Cost — i.e., consumer k flies high quality as long as Ik ≥ TF . Notice further that (7) implies that (6) binds at lower levels of income for the Low Cost carrier than for the Full Service carrier. In particular, as we normalized QL = 0, the condition for not staying at home, (6), TL . The above considerations taken altogether give rise to the demand schedule for reduces to Ik ≥ 1−Π Low Cost and Full Service carriers illustrated in Figure 1. Q.E.D. Proof of Proposition 1: Notice first that it is easy to show that ∂P/∂M < 0 in equilibrium — and, a fortiori, ∂Π/∂M < 0. This is a standard result with CES utility functions: as the variety of shops increases, the price of a unit of utility from goods consumption diminishes. Hence, the indirect utility function of traveler k, (5), clearly increases when M increases. More precisely, differentiating (14) with

30

respect to M yields −σ ∂UJk (σ − 1)τ −2 τσ−1 M = (Ik − TJ ) τ −1 ∂M (cσ)

1+M

τ −1 σ−1



σ−1 cσ

τ −1 ! 2−τ τ −1 > 0,

where the inequality follows from Ik > TJ and σ > 1. Second, consider expression (15), a shop profit expressed as a function of the extensive margin λ. Notice that λ is the income of the marginal traveler — i.e., the lowest income traveler — and it must therefore be greater or equal to TL . As λ increases, the income of the marginal traveler increases, that is less consumers decide to travel. In other words, the larger λ, the lower the number of shoppers brought to the destination by airline companies. To see this, differentiate (15) with respect to λ to get ∂π = −λ + TL ≤ 0. ∂λ Hence, the lower the number of potential shoppers the lower a shop profit, which proves the asserted two-sided nature of the market at hand. Q.E.D. Proof of Lemma 2: Clearly K > 0, Π > 0 and P > 0. Proof that K < Π. Suppose not. Then, substituting for K and Π it must be:  c (1 − ρ)  ρM

1−ρ ρ

 1−

1+

c ρ−1 M ρ ρ



ϕ ϕ−1

!−1  ϕ1



 >

1+

c ρ−1 M ρ ρ



ϕ ϕ−1

! ϕ−1 ϕ

.

(A8)

 ϕ   ρ−1  ϕ−1 c ρ Take first the power of ϕ and then multiply by 1 + ρ M both sides of (A8). Simplify the left hand side and get

(1 − ρ)

Now take the power of

1 ϕ

ϕ



c ρ−1 M ρ ρ



ϕ2 ϕ−1

 >

1+

c ρ−1 M ρ ρ



ϕ ϕ−1

!ϕ .

(A9)

on both sides of (A9) and simplify to get the following condition  −ρ

c ρ−1 M ρ ρ



ϕ ϕ−1

> 1,

which is clearly impossible given the admissible parameter values. Hence, it must be K < Π. Proof that Π < 1. Suppose not, then it must be Π−1 < 1. Substituting for Π, this implies  1+

c ρ−1 M ρ ρ



31

ϕ ϕ−1

! 1−ϕ ϕ

< 1.

(A10)

Take the (positive) power of

ϕ 1−ϕ

on both sides of (A10) and simplify to get 

c ρ−1 M ρ ρ



ϕ ϕ−1

< 0,

which is clearly impossible. Hence, it must be Π < 1. Proof that Π < P . Suppose not, then, substituting for P and Π, it must be 

c ρ−1 M ρ < ρ Take the power of

ϕ 1−ϕ

1+

c ρ−1 M ρ ρ



ϕ ϕ−1

! ϕ−1 ϕ

.

(A11)

< 1.

(A12)

on both sides of (A11) and rearrange to get 

c ρ−1 M ρ ρ



ϕ 1−ϕ

 1+

c ρ−1 M ρ ρ



ϕ ϕ−1

!

Expand and simplify (A12) to get 

c ρ−1 M ρ ρ



ϕ 1−ϕ

< 0,

which is never satisfied. Hence, it must be Π < P . Q.E.D. Proof of Proposition 2: the proof, trivial, is developed in the text. Equilibrium profits are reported in Table 1 below. Here we only show that equilibrium airfares correctly define demands as in Figure 1, TLC TLC that is 1 > TFC > 1−Π > 0. This follows immediately by observing that TFC = 12 and 1−Π = 41 . Q.E.D. Proof of Proposition 3: the proof, trivial, is developed in the text. Equilibrium profits, net of the fixed transfer, are reported in Table 1 below. Here we only show that equilibrium airfares correctly define TLL TLL demands as in Figure 1, that is 1 > TFL > 1−Π > 0. Clearly TFL = 21 < 1, while 1−Π > 0 as TLL > 0. 2

(1−Π) (Π−K) To see why TLL = 2(Π+(1−2Π)(Π−K)) > 0, notice first that the numerator is positive as K < Π < 1 by Lemma 2. As to the denominator, its sign depends on the sign of Π + (1 − 2Π) (Π − K) and, given Π < 1, we can write

Π + (1 − 2Π) (Π − K) > Π − (1 − 2 · 1) (Π − K) = K > 0. Hence, the denominator is positive as well as the numerator and we conclude that TLL > 0. What is left to be shown is that TFL > 1 > 2

TLL 1−Π .

This inequality reduces to

(1−Π)(Π−K) 2(Π+(1−2Π)(Π−K))

⇐⇒

1 > Π − K,

which is always true given Lemma 2. Q.E.D. Proof of Proposition 4: the proof, trivial, is developed in the text. Equilibrium profits, net of the 32

fixed transfer, are reported in Table 1 below. Here we only show that equilibrium airfares correctly TLF define demands as in Figure 1, that is 1 > TFF > 1−Π > 0. Applying Lemma 2 it follows immediately that both carriers airfares are positive, so that TLF 1−Π .

Let us then prove in turn that 1 > TFF and TFF > Π−K 1 > 2 3(Π−K)+Π(1−K)

⇐⇒

TLF 1−Π

> 0.

Indeed 1 > TFF if, and only if,

(Π − K) + Π (1 − K) > 0,

which clearly follows from Lemma 2. TLF TLF Next, let us prove that TFF > 1−Π . To this end, it suffices to notice that TFF = 2 1−Π , from which the result clearly follows. Q.E.D. Proof of Corollary 1: we make heavy use of Lemma 2, which we refer to “the lemma” for brevity. We proceed by sets of inequalities as they appear in the corollary. Proof that TLC > TLF > TLL . Start with TLC > TLF , which holds if, and only if, 1−Π 4

>

(1−Π)(Π−K) 3(Π−K)+Π(1−K)

⇐⇒

K (1 − Π) > 0,

which is true by the lemma. Next, consider the inequality TLF > TLL , which is true if, and only if, (1−Π)(Π−K) 3(Π−K)+Π(1−K)

>

(1−Π)2 (Π−K) 2(Π+(1−2Π)(Π−K))

⇐⇒

K (1 + Π (2 − Π)) > 0,

which is true by the lemma. Proof that TFC = TFL > TFF . The first relation is trivial as TFC = 21 = TFL . The second is true if, and only if, 1 Π−K > 2 3(Π−K)+Π(1−K) ⇐⇒ K (1 − Π) > 0, 2 which is true by the lemma. C F Proof that QL F > QF > QF . The first inequality is true if, and only if, 1−Π(Π−K) 2(Π+(1−2Π)(Π−K))

>

1+Π 4Π

⇐⇒

K (1 − Π) > 0,

which is true by the lemma. The second inequality is true if, and only if, 1+Π 4Π

>

1+Π Π−K Π 3(Π−K)+Π(1−K)

⇐⇒

K (1 − Π) > 0,

which is true by the lemma. Proof that πLL > πLC > πLF . The first inequality is true if, and only if (see Table 1), (1−Π)Π2 (1−Π+K)2 4(Π+(1−2Π)(Π−K))2

>

1−Π 16

⇐⇒

K (3K + 4 (1 − Π) (Π − K)) > 0,

33

which is true by the lemma. The second inequality is true if, and only if, 1−Π 16

>

(1−Π)(Π−K)2 (3(Π−K)+Π(1−K))2

⇐⇒

K (1 − Π) (Π (1 − K) + 7 (Π − K)) > 0,

which is true by the lemma. Proof that πFF > πFC = πFL . The second relation is trivial as πFC = and only if, (K−2Π+KΠ)2 (3(Π−K)+Π(1−K))2

>

1 4

⇐⇒

1 4

= πFL . The first inequality is true is,

K (1 − Π) (5 (Π − K) + 3Π (1 − K)) > 0,

which is true by the lemma. Q.E.D. Proof of Corollary 2: we make heavy use of Lemma 2, which we refer to “the lemma” for brevity. We proceed by sets of inequalities as they appear in the corollary. i , i ∈ {C, L, F }. The proof for market structures i = C, L is trivial: in fact, in these Proof that DFi > DL i i
i = T i − TL < 1 because TL ∈ 0, T i . As to the case cases TFi = 21 so that DFi = 1 − TFi = 12 while DL F F 1−Π 2 1−Π in which the Full Service carrier deals with the Mall, we have

DFF =

Π−K+Π(1−K) 3(Π−K)+Π(1−K)

F DL =

and

Π−K 3(Π−K)+Π(1−K) .

F reveals that, given the lemma, the former is larger A quick inspection of the expressions for DFF and DL than the latter.

Proof that DFF > DFC = DFL . The proof of the second relation is trivial: as stated above, DFC = The first inequality is true if, and only if, Π−K+Π(1−K) 3(Π−K)+Π(1−K)

>

1 2

⇐⇒

K (1 − Π) > 0,

which is true by the lemma. L > D C > D F . The Low Cost carrier demand in the different market structures is Proof that DL L L 1−(Π−K) L DL = Π 2(Π+(1−2Π)(Π−K)) ,

C DL =

1 4

and

F DL =

⇐⇒

K > 0,

Π−K 3(Π−K)+Π(1−K) .

The first inequality is true if, and only if, 1−(Π−K) Π 2(Π+(1−2Π)(Π−K)) >

1 4

which is always true by the lemma. The second inequality is true if, and only if, 1 4

>

Π−K 3(Π−K)+Π(1−K)

⇐⇒

which is always true by the lemma. 34

K (1 − Π) > 0,

1 2

= DFL .

Ti

L + D L > D F + D F > D C + D C . Notice first that D i + D i = 1 − L Proof that DL F L F L F L F 1−Π , i ∈ {C, L, F }. Hence, the result immediately follows from the fact that TLC > TLF > TLL (see Corollary 1). Q.E.D.

Proof of Proposition 5: the argument of the proof is illustrated in the main text before the proposition. The Mall will deal with the Low Cost carrier if, and only if, π L − πLF > π F − πFL . Substituting the values from previous proposition, this relation reduces to K (Π − K)

(8Π2 −Π4 −12Π+1)K 2 +Π(32Π−30Π2 +8Π3 +Π4 −7)K+8Π2 (1−Π)3 8Π(3(Π−K)+Π(1−K))2 (Π+(1−2Π)(Π−K))

> 0.

The sign of the LHS depends on the numerator of the fraction as, by Lemma 2, Π > K and the denominator is positive. Let’s denote the numerator as

f (K, Π) = 8Π2 − Π4 − 12Π + 1 K 2 + Π 32Π − 30Π2 + 8Π3 + Π4 − 7 K + 8Π2 (1 − Π)3 . Then contracting with the Low Cost is efficient if, and only if, f (K, Π) > 0. Notice now that f (K, Π) is a second degree polynomial in K with coefficients a (Π) =

8Π2 − Π4 − 12Π + 1




b (Π) = Π 32Π − 30Π2 + 8Π3 + Π4 − 7




c (Π) = 8Π2 (1 − Π)3 . Notice further that f (K, Π) is convex in K if, and only if, a (Π) > 0. In the parameter range Π ∈ (0, 1) there is a unique root of a(Π), which we call ξ, and it turns out that a(Π) > 0 if, and only if, Π < ξ with v s  u −1 q q q q u √ √ √ √ 1 t 3 3 3 3 ξ ≡ √ 16 + 18 6 143 + 78 3 + 143 − 78 3 + 8 − 143 + 78 3 − 143 − 78 3 + 6 r q q √ √ 1 3 3 −√ 8 + 143 + 78 3 + 143 − 78 3 ≈ 0.0885564. 6 Take first the case Π < ξ, i.e. f (K, Π) is convex. Then it has a minimum in b(Π) K min = − 2a(Π) =

Π(−32Π+30Π2 −8Π3 −Π4 +7) . 2(8Π2 −Π4 −12Π+1)

Notice now that K min > Π, in fact 2

3

4

+8Π −Π −5 Π − K min = Π 8Π−14Π < 0. 2(8Π2 −Π4 −12Π+1)

(A13)

To see this, notice first that the denominator of (A13) equals 2a (Π), which is positive because Π < ξ.

35

Focus then on the numerator. It can be written as
8Π (1 − Π)2 + Π2 2 − Π2 − 5, where, letting Π ∈ [0, 1], it is not difficult to show that the first addendum has a maximum in Π = 31 and 2 32 takes value 32 27 , while the second addendum has a maximum in Π = 3 and takes also value 27 . Hence, 32 49 the value of the numerator is bounded above by 2 27 − 5 = − 27 < 0, which proves that Π < K min . If this is so, then f (K, Π) is decreasing in K for any Π < ξ and, given that K is bounded above by Π, it takes a minimum in K = Π, which is lim f (K, Π) = 2Π2 (1 − Π)2 > 0.

K→Π

This proves that, for Π < ξ, the function f (K, Π) is positive in the relevant parameter range (K, Π) ∈ (0, Π) × (0, ξ). Take now Π > ξ so that f (K, Π) is a concave quadratic equation in K. Then we know that f (K, Π) is minimum at a corner, that is either at K = 0 or at K = Π. It therefore suffices to check that limK→Π f (K, Π) > 0 — which we already know from above — and that limK→0 f (K, Π) > 0 which is indeed true as lim f (K, Π) = 8Π2 (1 − Π)3 > 0. K→0

This last inequality proves that f (K, Π) > 0 for Π > ξ which completes the proof! Q.E.D. Proof of Proposition 6: we first prove that the consumer welfare is larger under Low Cost-Mall contracting than under the standard competition scenario. The consumer welfare, (17), reads CW =

1+2(1−TF )(ΠQF −TF ) 2Π

+

TL2 −2(1−Π)TL TF 2Π(1−Π)

.

Differentiating CW with respect to TL yields ∂CW ∂TL

=

TL −TF (1−Π) , Π(1−Π)

TL < TF in both scenarios by Propositions 2 and 3. Hence, because TLC > TLL which is negative because 1−Π by Corollary 1, CW is larger under Low Cost-Mall contracting than under standard competition. Finally, to prove that the joint profits of the carrier and the Mall are higher under Low Cost-Mall contracting than under the standard competition scenario, it is enough to calculate the profit differential by substituting equilibrium values of the airfares to get


π L + πF − πLC + πSC + πFC =

K2 32Π((2Π−K)(1−Π)+KΠ)

36

> 0.

Q.E.D.

Table 1: Equilibrium profits under different scenarios. Comp.

Low Cost/Mall coop.

Full Service/Mall coop.

πL

1−Π 16

(1−Π)Π2 (1−Π+K)2 4(Π+(1−2Π)(Π−K))

(1−Π)(Π−K)2 (3(Π−K)+Π(1−K))2

πF

1 4

1 4

πS

K 2Π+5 Π 32

K

2

(K−2Π+KΠ)2 (3(Π−K)+Π(1−K))2

K(2Π−1)((Π−K)(1−Π(2+Π))+Π(3−Π2 ))+Π2 (2Π+3)(1−Π)2 2

8Π(Π+(1−2Π)(Π−K))

37

K

Π2 (6Π+1)−(Π2 +4Π+2)(2Π−K)K 2Π(3(Π−K)+Π(1−K))2

Figure 3 below shows that the profits of the Low Cost carrier are decreasing in ϕ even when c is small or M is large.

0.06

0.06

0.04

0.04

0.02

0.02

0.00 1

0.00

0

ρ

1

ϕ

0

0

ρ

ϕ

1

0

(a) c = 1 and M = 10

1

(b) c = 1 and M = 50

0.06

0.06

0.04

0.04

0.02

0.02

0.00 1

0.00

0

ρ

1

ϕ

0

0

ρ

ϕ

1

0

(c) c = 0.1 and M = 10

1

(d) c = 0.1 and M = 50

Figure 3: πLE with changing c and M

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