1 Introduction 2. 2 Literature 2

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1 Contents 1 Introduction 2 2 Literature 2 3 Framework Monopoly Case Duopoly Case Airline and Platofrm demand Equilibrium Analysis Profit Analysis and Managerial Implications Profit Analysis Managerial Implication Conclusion 7 6 References 7 1

2 Platform Competition and Consumer Myopia: The Case of Airports ON-GOING WORK Giuseppe D Amico Abstract Consumers, when purchasing, may exhibit lacks of information over some attributes of the product or service they are paying for, this leads to a gap between the expected and the actual post-consumption consumer surplus. Optimal strategies of firms that sell core and side goods, airports are an example, can vary according with the extent of this bias. This work develops the model by Flores-Fillol et al (2017) and extends it to a duopoly setting by comparing the optimal behaviour of a monopoly platform with the case of two multi-product platforms competing à la Hotelling. The results about the optimal airport choices are consistent with Flores-Fillol et al (2017) and do not present any difference moving from the monopoly to the duopoly case. As the degree of myopia decreases, consumers value more the retail product leading the airport to change its strategy charging higher landing fees and allowing for a more competitive environment on the retail side. On the other side, the relationship between profits and the consumer myopia strictly depends on the considered market structure. In the monopoly case, airport profits are non-decreasing in the degree of myopia. Differently, in the duopoly case, a negative correlation between airport profits and myopia is observed. 1 Introduction 2 Literature 3 Framework The article provides a comparison of the airport optimal choices developed in two scenarios: monopoly and duopoly setting. Despite different, the two settings rely on a common theoretical framework that will be presented in this section, further specifications for the monopoly and duopoly case will be later explained. Platform structure In the considered model we observe a platform that provides essential inputs to the downstream market that serves the demand core and side services. More specifically, an airport rents its infrastructures to airlines and sets the number of concessions to award in the retail market. The airport-airline layout is structured as a bilateral monopoly where all the bargaining power is owned by the upstream firm. The size of the retail component is decided by the airport that, at a first stage, sets non-cooperatively and simultaneously the number of the available concessions to be awarded satisfying the condition: n i 2 for the i-th platform, furthermore market of concessions is supposed to be always clear whatever the number of setted concessions. The type of product sold by retailers is equally differentiated within each platform and its degree of differentiation is identified by the extent of the parameter s R ++. The airline market is dominated by a single carrier operating a single route with no traffic problems. 1 1 The aim of the paper is to underline how expectations over delayed consumption of add-ons affect the platform s business strategy and platform profits. 2

3 Consumers Consumers derive their utility from the consumption of aeronautical and non-aeronautical services. Their decision process is made up of two steps: first, they buy the flight ticket; second, they can benefit from the retail services once at the terminal. 2 We consider a continuum of passengers with a linear utility function of the form U(p A, p R ;z,δ) = z + δecs(p R ) p A, where p A is the ticket price and p R = (p 1, p 2,..., p nr ) is the vector of prices set by the n R retailers; z is the gross benefit passengers derive from travelling, travellers are uniquely identified by z that is, under standard assumption, uniformly distributed over the support [ a,1]; ECS(p R ) is the expected surplus each passenger derives from the consumption of the retail activity. In the end, δ [0,1] is the degree of myopia, its importance is given by the timing of the consumer decision-process. Flight decision is not an independent choice, consumers expect they will benefit of a certain surplus by accessing retail services, δ tells us the extent of this expectation. Each passenger can purchase at most one flight ticket and has a 0 outside option. Let z be the flight utility parameter of the consumer that is just indifferent between flying and not flying. Then, the aggregate demand for flights is whenever this is positive. Q A (p A, p R ;δ) = 1 z(p A, p R ;δ) = 1 p A + δecs(p R ), (1) Retailers structure and demand The n R retailers sell an homogeneous good and are symmetrically distributed on a Salop circle of length 1, with n R 2. As already discussed, the retail product is available only to that segment of demand that decides to make use of the airline services. The mass of potential consumers is Q A (p A, p R ). Each consumer has a unit demand and a taste parameter x for the retail good, which is uniformly distributed over the support [0,1] and is taken to be her position along the circle. For a consumer located at x, retail utility when buying from the nearby retail firm located in x i is u = v p i t x x i. We assume that v is always sufficiently high so that the market is fully served. As it will become clear at a later stage, this implies v > 5 t. (2) 8 Retailers demand and profits are derived in the standard way. Focus on retailer i, assumed w.l.o.g. to be located at 0, and consider that all rivals are symmetrically located. The marginal consumer between firm i and one of its nearest rivals, say firm j, is x i j = 1 2n R + p j p i 2t. Assuming symmetry in the prices set by all the rival firms to firm i, the demand for i becomes X i (p A, p R ) = 2 x i j (p i, p j )Q A (p A, p R ). After normalizing retailers costs to 0, retailer i s profits are ( 1 π i = p i X i (p A, p R ) = p i + p ) j p i [1 p A + δecs(p n R t R )]. (3) The above expression makes it clear that retail profits depend on the number of passengers which, in turn, depends on their retail surplus expectation. When deciding whether or not to buy the flight ticket, consumers are not yet aware of their taste parameter (the location x on the unit circle). In other words, a passenger does not know in advance whether she will want, say, to spend time in a restaurant for a meal or simply go to a bar for a coffee, as this depends on contingencies that cannot be foreseen when booking the flight. Only on the day of the flight, this will be revealed. Still, a passenger may anticipate she will want either a coffee or a meal on the day she flies. Therefore, passengers are able to form an expectation of the surplus they will be able to enjoy. Passengers 2 Hierarchy in consumption is a fundamental assumption: differently from the set-up used in Bracaglia et al, 2014, demand for the retail activities is just a fraction of the demand for flight. 3

4 priors consider that each location along the Salop circle is equally likely. Hence, the value of the expected surplus when one retailer charges p i and all other retailers charge symmetrically p j (let p j denote the vector of these prices) is CS ( ) p i, p j = v p j t + p j p i + (p j p i ) 2. (4) 4n R n R 2t This is the value that passengers may anticipate, according to their degree of foresight, δ, when booking a ticket. 3.1 Monopoly Case The monopoly case builds on the model developed in Flores-Fillol et al. (2017). The main differences with respect to their model are the assumption of passive rational expectations instead of fully rational expectations on the retail side a monopoly market structure in the airline business instead of having competition à la Cournot. 3 Equilibrium Analysis In this Section, we first analyse the second-stage equilibrium in which retailers and airlines choose their prices Then, we consider the first-stage equilibrium in which the airport chooses the extent of the landing fee and the number of retail concessions to be awarded. Second Stage: Retailers and Airline problem Retailers and the monopoly airline simultaneously choose prices and the optimal airfare they will charge passengers. Consumers exhibit passive rational expectations since they only observe retail prices once at the airport, but not before. As a consequence, the retailers price decisions do not affect this expectations; i.e., ECS(p i,p j ) p i = 0. In any case, passive expectations are rational and, therefore, they are fulfilled in equilibrium. Each retailer is involved in a symmetric price game with the other retailers, each agent maximises its profits, i.e., max pi π i ( pa, p i, p j ) = pi X i (p A, p i, p j ); identically, the monopoly airline chooses the equilibrium airfare by solving max pa π A (p A, p R ) = (p A l)q A (p A, p R ). In line with the literature, aeronautical services are sold to airlines at a uniform per-passenger landing fee l 0. 4 Lemma 1 By solving the simultaneous price game between airline and retailers we obtain the following equilibrium outcomes, i.e., p R (l,n R ) = t p A (l,n R ) = 1 + l n R 2 + δ ( v 5t ). (5) 2 4n R }{{} CS(n R ) In equilibrium, retailers set the standard symmetric Salop price, the reason is that the retailers know that their price decisions do not affect the consumer behaviour and, therefore, they act as if consumers were fully myopic. The result we have obtained for the monopoly airline is composed by a standard doublemarginalization term plus a mark-up that depends on the degree of consumer foresight and the equilibrium consumer surplus from retail activities. Therefore, as the retail surplus anticipated by consumers increases, the airline optimally responds by raising its equilibrium fare. Given the previous results, we can rewrite (1) and (4) as it follows, 3 The way the airline market is designed does not affect the airport choices at the first stage. A more fragmented structure decreases the demand for the single airline 4 Allowing for l < 0 would not change qualitatively our results. It can be interpreted as the aeronautical mark-up obtained by the airports. Therefore the case l < 0 corresponds to a situation in which the airport sets the fee below its marginal cost to attract more passengers with the ultimate purpose of boosting revenues from the retail activity. 4

5 CS(n R ) = v 5t 4n R, Q A (l,n R ) = 1 l 2 + δ ( v 5t ). (6) 2 4n R }{{} CS(n R ) The assumption in (2) guarantees that CS(n R ) is strictly positive. First Stage: Airport problem In the first stage, the airport maximises profits by setting the landing fee and choosing the number of concessions to award in the retail market, i.e. max l 0,n R 2 Π(l,n R ) = (l + p R )Q A (l,n R ). the airport is able to fully extract profits from retail activities and charge the airline company a per passenger landing fee for the use of the infrastructure. 5 Lemma 2 Let n R and l be the equilibrium landing fee and the optimal number of retailers allowed to operate at the terminal and let t 1 8(1+δv) 4+5δ. Then, for 0 < δ < t ( ) l n R = 2 + δ 2 v 5t 4n R i f t < t 1, n R = 2. (7) 0 i ft t 1, In making their flight decision, consumers exhibiting a high degree of myopia evaluate more the price of the ticket than the expected surplus from the add-on activities consumption. Such a system of weights allows the airport to extract, whenever possible, Therefore, the airport optimally acts by extracting as much and sets the price for the primary good below the monopoly price. 6 The high level of myopia forces the airport to act strategically using the primary good as a tool to expand its catchment area. 7. Lemma 3 Let n R and l be the equilibrium landing fee and the optimal number of retailers allowed to operate at the terminal. Then, for 4 5 < δ 1 l = 1 + δv, n R. (8) 2 As the degree of foresightedness increases, the consumer evaluation of the add-ons increases as well and the platform optimally reacts switching its strategy, expanding its catchment area through the secondary product and making profits through the core service. Airport decides to set the retail price at the marginal cost and to make no profits on this side of market in order to increase the consumer surplus on the retail side and boost the demand for flights and sets landing fee above the monopoly price. 8 Being interested in checking which is the best platform strategy, we can compare the platform profits when δ < 4 5 and δ > 4 5. Proposition 1 Under monopoly, platform profits are strictly increasing in consumer foresight, i.e., Π/ δ > 0. 5 Following Flores Fillol et al, (2018), concessions are awarded such that the retailers have no rights on a potential extra-profit, e.g., by means of a first-price auction. Our findings qualitatively holds also imposing a sharing-rule with the concessionaires earning positive profits. 6 Add parametric assumption for t. 7 Remarkable, as t 0 we observe the opposite behaviour: landing fee above the monopoly price and minimum number of retailers. Indeed, despite the maximal concentration p R 0 and the passengers will be attracted through the retail product 8 Effect of one way complementarity, try to add this 5

6 3.2 Duopoly Case In this section we will consider the presence of a competitor for the incumbent platform. Passengers in the previous model had a zero outside option, in this section travellers have the alternative of joining another airport, they have an heterogeneous scheme of preferences over the two terminals, but the possibility of staying outside the market has been ruled out. In the duopoly case we consider two platforms, structured as the one we have considered in the monopoly case, that compete à la Hotelling. 9 The timing of the game is the same used in the monopoly case: in the first stage, the competing airports simultaneously and non-cooperatively set the landing fee and the number of concessions to be awarded in the retail market; in the second stage, retailers and the monopoly airline in both platforms choose their prices; finally, travellers make their decision over which platform joining and payoffs are collected Airline and Platofrm demand Each facility, in this model, is considered to be exogenously endowed with one, different, characteristic that travellers evaluate -let s define with 0 the airport with higher quality connections and with 1 the airport served with relaxing areas- and consumers location over the line identifies the relative preference over these two features. Population is supposed to be unitary and let a parameter θ U[0,1] uniformly distributed on a support [0, 1] identify each passenger on the line over his relative preference about airport s characteristics - a consumer close to 0 will evaluate more airport connections than the massive presence of relaxing areas within the facility, vice versa a consumer close to 1 will give more weight to the possibility to have relax once in the airport. A consumer, in order to reach one of the platforms, incurs in a linear transport cost of slope s R ++, interestingly while in standard spatial airports models this cost represents literally a cost for the door-to-door transport, in this model this cost identifies the disutility a passenger bears for giving up one of the two characteristics - a consumer located close to 1 suffers a cost for joining a platform poorly connected with the centre, as we move to 1 passengers weight relatively more the presence of relaxing areas and consequently the extent of disutility decreases. Platform demand is worked out in the standard way. Traveller maximise the following utility function, i.e., U(p A, p R ;z,δ) = z + δe[cs] p A s θ i θ j. General considerations on z, δ, E[CS] and p A still hold from the monopoly case. The disutility the travellers incur moving from their position to the platform is identified by s; finally, θ i identifies the position of the passenger on the unit line. Recalling that in this framework, without loss of generality, the two competing platforms are located at the extremes [0, 1] of the unit line, it is possible to find the marginal consumer: ˆθ = p1 A p0 A + δ ( E[CS 0 ] E[CS 1 ] ) + 1 2s 2s 2. Since each individual is uniquely identified by his taste parameter, ˆθ identifies the demand for platform 0. It is possible to generalize this result by saying that the demand for the h-th platform is: Q h A(p A,p R ;δ) = pk A ph A + s + δ ( ) E[CS h ] E[CS k ] h={1,0}, h k (9) 2s 2s Retail structure remains unaltered from the monopoly case, retailers sell a homogeneous product the demand for the retail services is just a share of the total platform demand : Xi h(p A, p i, p j ;δ) = 2x i, j Q h A (p A,p R ;δ). 9 In most of the cases, spatial modelling in airport literature has been treated in a strictly geographical way. Actually, travellers may differ over the evaluation of the services they will find at the terminal, someone evaluates more land-connections and others may be more concerned on having relaxing areas at the terminal. In this model we endow each platform with an exclusive and not replicable feature whose evaluation is heterogeneous across the population. 6

7 3.2.2 Equilibrium Analysis Second Stage: Retail and Airline problem At this stage, retailers and airlines, in both platforms, are involved in a price game where they decide simultaneously how to charge the passengers. For a generic airport h, retailers and airlines maximise their ( profit function, respectively πi h (p A, p i, p j ;δ) = p h i X i h(p A, p i, p j ;δ) Q h A (p A,p R ;δ). and πa h (p A) = p h A l ) Q h A (p A,p R ;δ). Lemma 4 In a symmetric duopoly with fixed Hotelling competition, the optimal retail price is given by the standard Salop symmetric equilibrium outcome and the optimal airfare is composed by a standard Hotelling result and a component depending on δ, i.e., p h R(l,n h R) = t n h, p h A(l,n R ) = 3s + 2lh + l k + δ ( 5 t R n k t ) R n h. (10) R Retailers, independently of the platform market structure, set-up a standard Salop price. Passive rational expectations assumption ensures us retailers will not care about across and within platform competition, they do not play strategically and set a price for their service independent of the consumer myopia. Airlines compete à la Hotelling and charge an airfare that embodies part of the potential surplus the passengers gain from the retail side. 10 The assumption in (2) guarantees airline equilibrium outcome in (5) to be strictly greater of the perfectly myopic case, i.e., p A δ>0 > p A δ=0 because of the zero outside option assumption. The duopoly is characterised by a positive, and symmetric, outside option and it makes the effect of a δ marginal increase ambiguous, at this stage. First Stage: Airports problem At the first stage, both airports choose simultaneously the extent of the landing fee Proposition 2 Under duopoly, platform profits are weakly decreasing in consumer foresight, i.e., Π/ δ 0. 4 Profit Analysis and Managerial Implications 4.1 Profit Analysis In this section the evolution and composition of profits will be explained. 4.2 Managerial Implication Proposition 3 5 Conclusion 6 References Armstrong, M., Competition in two-sided markets. Rand Journal of Economics 37 (3), Barbot, C., 2009b. Airport and airlines competition: incentives for vertical collusion. Transportation Research Part B 43, Basso, L. J. and Zhang, A., Congestible facility rivalry in vertical structures. Journal of Urban 10 Outcomes from a symmetric model will be, of course, symmetric as well, but rethinking this model by imposing an asymmetry into the platform competition could provide less naive results 7

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