'AIRPORT COMPETITION: CONNECTING TIME ... - Wiley Online Library

HUB-AIRPORT COMPETITION: CONNECTING TIME DIFFERENTIATION AND CONCESSION CONSUMPTION* MING HSIN LIN Chukyo University This paper develops a network model to analyse the economic effects resulting from the non-price competition between the home country’s and neighbouring country’s hub-airports. Focusing on the tradeoff relationship between the length of the connecting time in the hub-airport and the consumption opportunities of the transfer passengers, we demonstrate theoretically that even though the hub-airport bears a cost disadvantage over its rival in providing the hub-airport service, it still has a chance to earn more profits than its rival by the setting of the connecting time. This finding suggests a new methodology for hub-airports that attempt to alleviate price competition. Keywords hub-spoke :network, hub-airport, connecting time, concession consumption

I.

Introduction

After airline deregulation, air carriers transform their networks into the hub-spoke type for cost-saving and strategic reasons1. At present, most airlines have adopted a hub-spoke type network (see Spiller, 1989; Zhang & Wei, 1993; Oum et al., 1995; Zhang, 1996; among many others). In a simple network linking one hub-airport and two spoke-airports, the hub-airport is in a monopoly position. But due to the development of multiple airlines networking, another hub-airport establishing links to these two spoke-airports becomes possible. In this case, the original hub-airport will compete against the potential hub-airport in the connecting flight market. With the dramatic growth of hub-spoke networks, hub-airport competition has become more common in many areas in the world (see Langner, 1996, p. 23; Rietveld & Brons, 2001). For example, in Asia Pacific, passengers travelling between Sapporo (a local city in the north of Japan) and Sydney may choose to fly through one of Japan major airports; e.g. Tokyo Narita, or to fly through Korea’s major airport; Seoul Incheon. A European example can be given by the connecting flight market between Dublin-Luxembourg where the transfer passengers may choose Amsterdam Schiphol or Paris Charles De Gaulle to transfer. In hub-airport competition, one of the strategic variables of the hub-airports is price, strictly speaking, the passenger charge or the landing/taking-off fee. However, compared to the Correspondence: Graduate School of Economics, Chukyo University, 101-2, Yagoto-honmachi, Showa-ku, Nagoya, 466 – 8666 Japan [email protected] * My grateful thanks are due to Nobuhiro Okuno, Hikaru Ogawa, Jiro Nemoto, Kazutoshi Miyazawa, Tatsuaki Kuroda, Takaji Suzuki, two anonymous referees and the editor (Professor D. Leonard) for their helpful comments and suggestions. I thank Richard Berry for his careful proofreading and helpful comments. My thanks also go to Kazuhiro Ohta of Senshu University for his remarks made on this paper at the 18th Annual conference of the ARSC (Applied Regional Science Conference) at Kitakyushu International Conference Center, 12 December 2004. 1 The cost advantage of the hub-spoke network has been argued by Bittlingmayer (1990), and Brueckner and Spiller (1991). Hendricks et al. (1995) indicated that the reason for the emergence of hub-spoke networks is the economies of density. Oum et al. (1995) asserted that besides the cost saving, switching from a linear to a hub-spoke network is a dominant strategy in an oligopolistic setting and will be useful in deterring entry. © Blackwell Publishing Ltd / University of Adelaide and Flinders University 2006.

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neighbouring country’s hub-airport, if the home country’s hub-airport bears a cost disadvantage in providing the airport services2, the home country’s hub-airport would naturally seek to differentiate its own airport services to alleviate the price competition (for example, as argued in Tirole (1988) and Borenstein and Netz (1999)). When considering the non-price competition between hub-airports, one essential focus is on the quality of the hub-airport services. Bruinsma et al. (2000, pp. 278–9) indicates that in a transfer market, passengers will pay attention to two quality aspects of the aviation services: services offered by the airlines using the airport (e.g. air-fares, frequencies, convenient departure times, etc.), and the additional concession goods/services of the airport such as tax-free shopping, restaurants, internet facilities, casino, etc. Bruinsma et al. (2000) addresses the former quality aspect from a generalised cost perspective, while the latter quality aspect concerning concession goods/services is not included. In this stream of analysis, Rietveld and Brons (2001) address the role of connecting (waiting) time at the hub-airport, focusing on the frequencies and the timetable co-ordination of the flights. The concession aspect of airports in which travellers can purchase goods/services in the airport is not considered. In the above two studies where the concession goods/services (hereafter, called concession goods) are not considered, the connecting time at the hub-airport has only a negative effect on the transfer passengers. Thus, the airport and airlines have an incentive to shorten the length of the connecting time to minimise the generalised cost (also see Encaoua et al., 1996). However, in a situation where the concession activities of the hub-airport are taken into account, shortening the length of the connecting time would decrease the transfer passengers’ consumption opportunities of concession goods. Smooth transits achieved on minimum connecting times mean less opportunity to spend money in hub-airport shops (see Hanlon, 1999, p. 156). Intuitively, there exists a trade-off relationship between the length of the connecting time and the consumption opportunities in the hub-airport. Thus, besides the described negative effects, the length of the connecting time seems likely to have a positive effect on the levels of concession revenues. Moreover, concession revenue accounted for a high per cent of total revenue in many major airports. For example, concession revenue at Hong Kong International Airport in the late 1980s and 1990s accounted for 66 –70 per cent of total revenue (Zhang & Zhang, 1997). Also, Jones et al. (1993) showed that in 1990 –1991, 60 per cent of the British Airports Authority and its agents’ total revenue came from commercial activities. Further, Doganis (1992) reported that in medium to large US airports, commercial operations had contributed 75–80 per cent of total airport revenue. It is therefore important to take into account the issue of concession activities when discussing hub-airport competition. Focusing on the trade-off relationship between the length of the connecting time and the consumption opportunities in the hub-airport, this paper attempts to develop a new hub-airport competition model to analyse the economic welfare effects when a hub-airport with a cost disadvantage (such as Japanese hub-airports) differentiates its services from its competitor by the setting of the connecting time. In our network model, both countries’ hub-airports and their major airlines (the national flag carriers) compete in the connecting flight market. The transfer passengers, first, make the decision of the routing choice (via-home country or via-neighbouring country) by observing the generalised price of each routing. And then, after the arrival at the hub-airport, the passengers make a decision concerning the consumption of the concession goods, given the length of the connecting time and the price of the concession goods. The two airlines compete in the Bertrand-Nash fashion, taking the length of the connecting time in the hub-airport as given. 2

It is well indicated that the airport charge and the landing/taking-off fee in Japanese major airports are much higher than those in neighbouring countries. This cost disadvantage may result from some geographical or technological reasons. For example, the constraint of land, or the high level of wage costs (Kuroda & Yagi, 1999). © Blackwell Publishing Ltd / University of Adelaide and Flinders University 2006.

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The concession goods are taken as being provided by each hub-airport itself. Each hub-airport chooses the length of the connecting time to maximise the total profits obtained from both concession and aeronautical activities. Under the above framework and the situation where the home country’s hub-airport bears a cost disadvantage in providing the airport services, we demonstrate theoretically that if both hub-airports set the length of the connecting time simultaneously, the home country’s hub-airport will set the connecting time longer, and will obtain a smaller total profit than its rival hub-airport. However, as another available strategy for differentiation, if both hub-airports can endogenously choose the role of Stackelberg leader or follower for the connecting time setting, multiple Stackelberg equilibria exist. In the equilibrium where the home country’s hub-airport acts as a follower and its rival acts as a leader, the home country’s hub-airport does obtain larger total profits than its rival (in other words, the home country’s hub-airport enjoys the second mover advantage) when the cost disadvantage is not sufficiently large. Existing literatures where the effects of concession revenue on pricing and/or economic regulation are argued include those by Zhang and Zhang (1997), Zhang and Zhang (2003), Lu and Pagliari (2004), and Oum et al. (2004). On the other hand, Hsu and Chao (2005) examines the relationship between concession revenue, passenger service level and space allocation in international passenger terminals. However, in spite of the increasing hub-airport competition, theoretical works concerning the competition between multiple hub-airports is relatively rare. Kuroda and Yagi (1999) examines a specific situation in which neighbouring countries’ hub-airports compete to become an international hub-airport, focusing on the airport financial system but the activities of airlines are not included in their model. Lin (2003) analyses the economic effects resulting from hub-airport competition and the corresponding airline competition by comparing the equilibrium of a monopoly-hub network with the equilibrium of an inter-hub network. The present paper contributes to the literature in developing a new model in which non-price competition between two hub-airports, price competition between their major airlines, and the concession consumption of the transfer passengers in the hub-airport are formulated. The findings of this model provide a new methodology for hub-airport competition. This paper is organised as follows. In Section II the inter-hub network model is constructed. In Sction III the demand for the connecting flight services and the equilibrium of the airline competition are derived in two sub-sections. In Section IV the behaviour of the demand side and supply side for the concession goods are presented. In Section V, the equilibrium of the hubairport competition where each hub-airport sets the length of the connecting time simultaneously is derived and the characteristics of the equilibrium are discussed. In Section VI the endogenous Stackelberg equilibria are derived, and the characteristics of each equilibrium are discussed. Concluding remarks follow in Section VII.

II.

Inter-hub Network Model

In the inter-hub network depicted in Figure 1, city B is located in country J (say the home country) and city D is located in country K (say the neighbouring country). Airline 1 is country J’s national flag carrier and it operates the connecting flights between city A and C using city B as its hub. On the other side, airline 2 is country K’s national flag carrier and it operates the connecting flights between city A and C using city D as its hub. The connecting passengers travelling between cities A and C can either fly through hub-airport B on airline 1, or fly through hub-airport D on airline 2. In the previous Asia Pacific example, B corresponds to © Blackwell Publishing Ltd / University of Adelaide and Flinders University 2006.

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Figure 1.


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Inter-hub network

Tokyo Narita, and D to Seoul Incheon. Correspondingly, airline 1 may be Japan Airlines, and airline 2 may be Korean Airlines. The connecting city-pair can be Sapporo-Sydney, or some other appropriate connecting city-pairs. In the previous European example, B corresponds to Paris and D to Amsterdam. Correspondingly, airline 1 may be Air France, and airline 2 may be KLM. The connecting city-pair can be Dublin-Luxembourg. There are no known direct flights between the above two given city-pairs, however it is possible for there to be more than two competing hub-airports. For ease of analysis, the network model deals only with the competition between two hub-airports. Moreover, in the given city-pair markets, the passengers may be able to choose different routings by interlining. For example, the passengers between Sapporo-Sydney may interline from Japan airlines to Qantas Airways at Tokyo Narita, or interline from Korean airlines to Qantas Airways at Seoul Incheon. However we will assume that passengers prefer on-line connecting services to interline connecting services. This assumption has been done in Park (1997). The network of this type is similar to the inter-hub network developed by Brueckner and Spiller (1991), and has been used by Zhang and Wei (1993) and Zhang (1996). Except the hub-airports and the connecting AC market, there are two spoke-airports and four direct city-pair markets in the network. To concentrate on the analysis of hub-airport competition, the activities of the two spoke airports are taken as being outside of the model. Further, since concession consumption of the direct flight passengers is not related to the length of the connecting time in the hub-airport, only the connecting market is considered. The three economic agents in our inter-hub network (the connecting passengers, airlines and hub-airports) will behave as follows. The connecting passengers, first, make the decision of flying through hub-airport B on airline 1, or flying through hub-airport D on airline 2 based on their generalised price which consists of air-fare and the connecting time. And then, when they reach the hub-airport, the passengers make a consumption decision of the concession goods, given the length of the connecting time and the price of the concession goods. Airline 1 and airline 2 compete in the connecting flight market by setting their own air-fare simultaneously, taking the length of the connecting time in the hub-airport as given. Hub-airport B and hub-airport D with both concession and aeronautical operations choose the length of the connecting time to maximise their own total profits3. 3

The hub-airport may choose the length of connecting time by coordinating the arrival and departure time of the connecting flight or by coordinating the departure time only, given the arrival time of the connecting flight.

© Blackwell Publishing Ltd / University of Adelaide and Flinders University 2006.

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III.

303

Demand for Connecting Flight Services and Airline Competition

a) Demand for connecting flight services Following the definition by Encaoua et al. (1996), the generalised price of each routing (via-home country routing and via-neighbouring country routing) is defined respectively as follows. GB ≡ s1 + b ⋅ lB2

(1)

GD ≡ s2 + b ⋅ l

(2)

2 D

where si(i = 1, 2) represents the air-fare of airline i, and lj(> 0, j = B, D) represents the length of the connecting time of hub-airport j. lj will be determined in the hub-airport competition stage (Section V). The parameter b(> 0) measures the monetary valuation of the passengers’ disutility caused by the connecting (waiting) time4. Besides the generalised prices, we assume that the connecting passengers exhibit brand loyalty to a particular routing5. Further, the reservation price of the connecting passengers is assumed to be large enough to insure that each passenger will purchase one connecting flight ticket. Each passenger makes the decision as to which routing to take. Under the above assumptions and using the specification provided by Brueckner and Whalen (2000), the demand of each routing can be derived as follows. It is assumed that a given connecting passenger will fly through their home country (hub-airport B) if the generalised price satisfies GB < GD + a or (a > GB − GD), where a gives the passenger’s monetary preference for via-home country routing. If a is uniformly distributed over the interval [−α/2, α/2], then the demand of via-home country routing is equal to α 2

X1 =

GB − GD

1 1 G − GD 1 s1 − s2 b(lB2 − lD2 ) da = − B = − − α α α α 2 2

(3)

the demand of via-neighbouring country is then X2 =

1 GB − GD 1 s1 − s2 b(lB2 − lD2 ) + = + + α α α 2 2

(4)

Note that one feature of this formulation is that the total demand of the connecting market is always equal to one. Generalised price differences serve only to divide this fixed total demand between the two routings. Another feature can be seen from (3) and (4), i.e. a small value α (a tight distribution of passenger’s preferences) makes the demand highly price sensitive6. 4

As we can see below (in Table I), the results in the airline competition stage are qualitatively the same in the case where the generalised price is a linear function of the connecting time. However, as we will see in Section VI (equations (12)-(15)), the quadratic function is more tractable than the linear one for solving the optimisation problem for the hub-airports. 5 The brand loyalty to a particular routing may emerge from the different schedule delay time costs if the departure time of airline 1 and airline 2 are different. In this explanation, the present definition of the generalised price will be consistent with Encaoua et al. (1996). The different lengths of the total flying time excepting the connecting time in the hub-airport between the two routings, as well as each airline’s different in-flight meals or language announcements may also cause the passengers to exhibit brand loyalty. 6 As an alternative specification (originally due to Hotelling, 1929), we can include another parameter that measures the monetary valuation of brand loyalty into the generalised price function (equations (1) and (2)). By assuming that the added parameter is uniformly distributed over the interval [0, 1], the demand functions like equations (3) and (4) can be derived from the indifferent condition between the two routings. © Blackwell Publishing Ltd / University of Adelaide and Flinders University 2006.

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b) Airline competition In this sub-section, the competition between airline 1 and airline 2 is considered. Similar to the assumption that has been made in the literature on airline competition (e.g. Pels et al., 1997; Hendricks et al., 1997), the simple Bertrand-Nash competition without capacity constraint is supposed here as well. For simplicity, we also assume that airline 1 and airline 2 operate only one connecting flight each day. Although both price/quantity, departure time, and flight frequency may be the desired policy variables in an airline competition model, as we can see in previous literatures, usually only one or two of these factors is chosen as the policy variable depending on the purpose of the analysis. Since this present paper focuses on the trade-off relationship between the length of the connecting time and the consumption opportunities of concession goods in the hub-airports, moreover, because frequency is fixed at least in the short run (Pels et al., 1997), we suppose that each airline operates only one connecting flight each day. This supposition is the same as Encaoua et al. (1996). Given the air-fare of its rival and the length of the connecting time of both hub-airports, each airline sets its air-fare to maximise its own profits. Specifically, the profit-maximising problems for airlines 1 and airline 2 can be posed as follows, respectively. Max

Π1 = s1 ⋅ X 1 − c1 ⋅ X 1 − FB

(5)

Max

Π 2 = s2 ⋅ X 2 − c2 ⋅ X 2 − FD

(6)

S1

S2

where ci(i = 1, 2) is the marginal cost of airline i, and Fj ( j = B, D) is the landing/taking-off-fee of hubairport j7. For the convenience of calculation, let us assume that ci ≡ 08. Solving the profit-maximising problems of these two airlines, we have the equilibrium shown in Table I (see Appendix A).

IV.

Demand and Supply of Concession Goods and Services

In this section we try to model the behaviour of the demand side and supply side for the concession goods in the hub-airports. Let us start from the demand side. Because of incomplete information, we essentially assume that the demand for the connecting flight and the demand for concession goods are independent. Namely, the passengers first, decide which route to choose by observing the generalised price of each routing. Second, after the arrival at the hub-airport, the passengers make a decision concerning the consumption of the concession goods, given the length of the connecting time and the price of the concession goods9. For simplicity, let us assume that all passengers arriving at each hub-airport are homogenous. The representative passenger at each hub-airport chooses both the length of the rest time and the consumption of concession goods to maximise their utility, subject to the budget constraint and the connecting time constraint. It is assumed that the utility of the passenger can be shown 7

As described in the introduction, the concern of this paper is on the non-price competition rather than on the price competition between hub-airports. Under the assumption that the frequency of each airline is fixed in the short run, the landing/taking-off-fee of the hub-airport is a fixed cost to the airline and thus has no effect on the behaviour of the airlines. Note that in a long run analysis, the landing/taking-off-fee of hub-airports may have an effect on the frequency choice of airlines, and may have an impact on the setting of the connecting time. 8 The simplification that the marginal cost is zero has been made in duopoly studies where products of firms are differentiated. The results are identical for positive constant marginal cost, where ‘air-fare’ is reinterpreted as the difference between air-fare and marginal cost. 9 One justification for this assumption (which has been argued by Zhang and Zhang (1997, p. 292)) can be provided by the fact that for most passengers, the purchase of an air ticket and the purchase of concession goods are well separated in time. © Blackwell Publishing Ltd / University of Adelaide and Flinders University 2006.

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by a quasi-linear function as U(q, r, y) = v(q, r) + y, where q represents the demand for the concession goods, r represents the length of the rest time in the hub-airport, and y is the expenditure for the consumption in the destination. Then the budget constraint to the passenger is p · q + y = m, where p is the price of the concession goods, m is the given income. Further, applying the concept created by De Vany (1974), we assume that the consumption of each unit of concession goods requires t(t ≡ 1) units of time. Thus the time constraint to the passenger staying at hub-airport j for connecting is r + t · q = lj. It should be noted here that the passengers may not spend all of the constant connecting time (lj) on consuming the concession goods. After leaving the aircraft, the passengers may spend parts of the connecting time to take a rest for recovering. Therefore, it seems natural to consider that the passenger’s utility increases as the length of the rest time increases. More importantly, the passengers choose the length of the rest time, given the length of the connecting time. Thus, a passenger choosing a longer rest time does not mean they will choose a longer connecting time10. According to this consideration, we impose the usual assumptions on the function v(q, r): increasing in q and r, and a diminishing marginal rate of substitution11. To make conclusions definitive, let us specify the quasi-linear utility function to U(q, r, y) ≡ q · r + y. Then solving the optimisation problem, we have the following demand function for the concession goods provided at hub-airport B. qB = 1/2 · (lB − pB)

(7)

Similarly, the demand function for the concession goods provided at hub-airport D is qD = 1/2 · (lD − pD)

(8)

where subscripts stand for the variable related to the hub-airport. On the supply side, it is supposed that the concession goods are provided by the hub-airport itself12. Hub-airport j( j = B, D) chooses the level of production for concession goods to maximise the profits obtained from the commercial activities (hereafter, called concession profits) given the demand function and the length of the connecting time. The profit-maximisation problem of hub-airport j is specified as follows. Max π j ≡ q j ⋅ (l j − 2q j ) − m j ⋅ q j qj

(9)

where mj is the marginal cost. Let us further assume mj ≡ 0 for reason of convenience. Solving the concession profit-maximisation problem, the optimal level of production can be shown as q mj = l j /4 . And the corresponding concession profits of hub-airport j are π mj = l 2j /8.

V.

Non-price Competition between the Hub-airports

Although recently some countries including the UK, Canada, Australia and New Zealand have adopted new policies to de-federalise or even to privatise some of their major airports, airports 10

Recall that the passengers have already borne disutility caused by the connecting time (equations (1) and (2)) in the routing choice stage. 11 The sufficient conditions for a diminishing marginal rate of substitution (i.e. the second order condition for the utility maximisation problem) are vqq ≤ 0, vrr ≤ 0, and vqr > 0. Solving the above optimisation problem, we have the demand function for the concession goods as q*(l, p). Comparative statics analysis shows that ∂q*(l , p )/∂l > 0 , as the second conditions are satisfied. 12 Under the assumption where the passengers make two separate decisions throughout the time of their travel, the result will be identical when the concession goods are provided by a monopolist in the hub-airport since the level of production for concession goods is decided independently to its rival. © Blackwell Publishing Ltd / University of Adelaide and Flinders University 2006.

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in many countries today are in public ownership13. In our study, we assume that the hubairports are publicly owned. As Langner (1996, p. 23) indicated that the main task of hubairports is to process passengers from one spoke-airport to another, it seems plausible to consider that hub-airports do not care about the origin and destination of the passengers. Thus let us further assume that hub-airports have no concerns about the consumer surplus of the passengers14. Now in this section, we discuss the determination of the length of the connecting time in both hub-airports, under the assumption that the home country’s hub-airport bears a cost disadvantage in providing the airport services. It should be noted that even though in practice, the length of the connecting times will be basically determined through a series of bilateral negotiations between airlines and airport authorities, there are different models that are related with this determination. In Encaoua et al. (1996), the behaviour of the hub-airport is not modelled and the length of the connecting time is indirectly determined by the airlines’ arrival and departure times in the hub-airport, which are supposed to be chosen by the airlines themselves. On the other hand, Rietveld and Brons (2001) argued that the length of the connecting time typically depends on both the flight frequency, and the timetable co-ordination of the flights. In our study, we will implicitly assume that the length of the connecting time is determined by the hub-airport and its major airline due to the assumption that hub-airports have concerns about the profits of their major airlines as well as their own concession and aeronautical profits. The major reason for the hub-airport to take the airline’s profits into account is because the airlines are the major source of passengers for the airport. Moreover, the hub-airport may worry that its major airline will leave if it cannot obtain a certain level of profits. Specifically, the optimisation problem of hub-airport j can be formulated as: Max W j ≡ Π j + ( F j − θ j ⋅ X iA )

(10)

s.t. (Π iA − F j ) ≥ 1 i

(11)

lj

Where Π j (≡ X ⋅ π ) is the total concession profits of hub-airport j( j = B, D), and ( F j − θ j ⋅ X iA ) is the aeronautical profits of hub-airport j with θj represents the marginal operating cost of hub-airport j’s service. In the constraint equation (11), (Π iA − F j ) is the net profit of airline i(i = 1, 2), and 1i(≥ 0) is a certain level of airline i’s profits, which insures that the airline will not leave the hub-airport j. Here, we can rewrite equation (11) as to F j ≤ Π iA − 1 i , and obviously know that the optimal landing/taking-off fee for hub-airport j is F j = Π iA − 1 i . Without losing generality, let 1i ≡ 0 and substitute F j = Π iA into equation (10), the objective function of hub-airport j can be rewritten as W j ≡ Π j + Π iA − θ j ⋅ X iA. Note that when j = B, i = 1, and when j = D, i = 2. Now, the above optimisation problem for each hub-airport can be rearranged by substituting the value of the equilibrium in the airline competition stage (Table I) into the objective function, respectively. They are A i

m j

Max WB =

1 ⎡α b(lB2 − lD2 ) ⎤ ⎡ α b(lB2 − lD2 ) l2 ⎤ ⋅⎢ − − θB + B ⎥ ⎥⋅⎢ − 3 3 8⎦ α ⎣2 ⎦ ⎣2

(12)

Max WD =

1 α

⎡α b(lB2 − lD2 ) ⎤ ⎡ α b(lB2 − lD2 ) l2 ⎤ ⋅⎢ + − θD + D ⎥ ⎥⋅⎢ + 3 3 8⎦ ⎣2 ⎦ ⎣2

(13)

lB

lD

13

For the ownership of major airports in regions of Asia Pacific, Europe and North America, Table 1 in Oum et al. (2004) is useful. 14 This assumption seems realistic. In fact, in Asia Pacific and Europe, hub-airport authorities argue that they are trying to maximise passenger traffic and do not care about the nationality of passengers. © Blackwell Publishing Ltd / University of Adelaide and Flinders University 2006.

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As stated earlier the home country’s airport bears a cost disadvantage, so let us assume θB > θD. Under the supposition that each hub-airport simultaneously chooses the length of the connecting time, the first order condition to each optimisation problem can be obtained as follows.

∂ WJ l ⎧ 3 − 16b b(6 − 16b) 2 b(3 − 16b) 2 2b ⎫ lB + lD + θ B ⎬ = 0 = B⎨ α − ∂ lB α ⎩ 24 36 36 3 ⎭

(14)

⎧ 3 − 16b b(3 − 16b) 2 b(6 − 16b) 2 2b ⎫ lB − lD + θ D ⎬ = 0 α + ⎨ 36 36 3 ⎭ ⎩ 24

(15)

∂ WK l = D ∂ lD α

Solving the equation system of (14) and (15), we have the FF equilibrium shown in Table II (see Appendix A) where FF stands for each hub-airport acting simultaneously15. From Table II, we have the following lemma: Lemma 1. In the FF equilibrium where each hub-airport sets the length of the connecting time simultaneously; a) the hub-airport with a cost disadvantage in the provision of the hub-airport service, sets the connecting time longer than its rival does. b) the total profits of the hub-airport with the cost disadvantage is smaller than that of its rival hub-airport. Proof:

for lemma 1-a, we have lB2 − lD2 = [24(θ B − θ D )]/(9 − 32b) > 0 from Table II. for lemma 1-b, follows directly from Table II. FF

FF

Lemma 1 can be explained as follows. Recall that each hub-airport maximises the total profits including the aeronautical and concession profits, taking its major airline’s profits into account. Setting the connecting time longer will decrease the gross profit of its airline since both air-fare and demand of passengers decrease, but will increase the demand for concession goods and increase the concession profits per passenger. For the hub-airport bearing the cost disadvantage, setting the connecting time longer to make more profits from the concession goods is more desirable than capturing more passengers to obtain the profits from the airline. Thus lemma 1-a holds16. Due to the cost disadvantage, the home country’s hub-airport makes a smaller total profit than the neighbouring country’s hub-airport.

VI.

Endogenous Stackelberg Equilibria in the Hub Airport Competition

In this section, we consider another available strategy for differentiation: choosing the role of Stackelberg leader/follower on setting the length of the connecting time. The motivation for extending our analysis to the endogenous Stackelberg type comes from that our study substantially applies the model of spatial product differentiation. Specifically, if we note that the length of the connecting time is indirectly determined by the arrival/departure time at the hub-airport (see footnote 3), we can regard our model as that hub-airports compete on the In the FF equilibrium, the sufficient condition for l 2j > 0 is b < 3/16, and the positive condition for air-fares (and the demand of the connecting flight) is ( θB − θD) ≡ ∆θ < (9 − 32b)α /16b ≡ ∆1. It can be confirmed easily that the second order condition to the optimisation problem is satisfied for any b < 3/16. 16 Since the focus is on the concession consumption of the connecting passengers, the transfer time costs to the airlines is ignored in our study. Conjecturably, if this effect is taken into account, the optimal length of the connecting should be shortened. 15

FF


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setting of departure time (given their own major airline’s arrival time) in the first stage; major airlines compete on price in the second stage17. Furthermore, in the general spatial competition models, firms are commonly assumed to behave under either the Stackelberg or Nash supposition in the location/price competition stage. Prescott and Visscher (1977) apply the concept of leadership in a spatial model where firms locate sequentially in the market, taken price as exogenously fixed. Anderson (1987) extends the Prescott-Visscher analysis for the two firms case to treat prices as endogenous. Teraoka et al. (2003) consider a Stackelberg type location game in which the roles of leader/follower are exogenously given. In the airline study by Encaoua et al. (1996), both Nash and Stackelberg suppositions have been done in the departure time competition stage. In their analysis, given the asymmetry of their network configuration, it is exogenously assumed that a hub carrier acts as a Stackelberg leader and a single-spoke carrier acts as the follower. Given the above observations on the spatial competition and airline studies, it seems desirable to consider a Stackelberg type location as well as the Nash fashion. Moreover, since there is no obvious reason to force which hub-airport acts as the location leader/follower in our model, let us consider the possible roles-choosing for the setting of the connecting time. Applying the endogenous Stackelberg leader/follower approach by Dowrick (1986), Furth and Kovenock (1993), and Lin (2004), we construct a role-choosing game where both hub-airport B and hub-airport D announce independently to act as a Stackelberg leader or a follower to choose the length of the connecting time, by setting the departure time of the connecting flight. It is assumed that the hub-airport who chooses to act as the leader commits itself to set the length of the connecting time, taking the reaction function of the follower into account; the hub-airport who chooses to act as the follower commits itself to follow its rival’s decision18. Thus there are four possible cases to this game. LF-case: hub-airport B chooses to act as the leader and hub-airport D chooses to act as the follower. FL-case: hub-airport B chooses to act as the follower and hub-airport D chooses to act as the leader. FF-case: both two players choose to act as the follower. LL-case: both two players choose to act as the leader. Now we will proceed to derive the outcomes for each case, respectively, then using these outcomes to argue the existence of the endogenous Stackelberg equilibrium. The outcome of the FF-case has been done in the previous section. The outcomes of the remaining cases will be derived as follows. First, we have the reaction function of each hub-airport from (14) and (15). They are shown as (16) and (17) respectively. RB : lB2 =

3(3 − 16b) 24 3 − 16b 2 ⋅α + ⋅ θB + ⋅ lD 2b(6 − 16b) 6 − 16b (6 − 16b)

(16)

RD : lD2 =

3(3 − 16b) 24 3 − 16b 2 ⋅α + ⋅ θD + ⋅ lB 2b(6 − 16b) 6 − 16b (6 − 16b)

(17)

For the LF-case, we can substitute the reaction function of the follower (equation 17) into the objective function of the leader (equation 12). Then, derive the first order condition for the leader. Solving this first order condition to obtain the optimal value of the length of the connecting time for the leader. This optimal value is represented by lB2 in Table III (Tables III–V LF

17

For previous studies that apply the location theory to airline industry see Panzer (1979), Encaoua et al. (1996), Borenstein and Netz (1999) and Salvanes et al. (2005). In particular, Borenstein and Netz (1999, p. 612) indicate that the scheduling of flight departure times provide a natural empirical test of spatial competition theories. 18 In practice, the length of the connecting time of the rival hub-airport can be cognised by observing its major airline’s arrival/departure time. © Blackwell Publishing Ltd / University of Adelaide and Flinders University 2006.

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LF

can be found in Appendix A). Substituting lB2 into the reaction function of the follower to obtain the optimal value for the follower (it is represented by lD2 in Table III). The other corresponding equilibrium values are listed in Table 3. Similarly, the outcome for the FL-case (which is shown in Table IV) can be derived by the inverse way. In the LL-case where both hub-airports choose to act as the leader, following Henderson and Quandt (1980), and Dowrick (1986), we have Stackelberg warfare19. The outcome for the LL-case is listed in Table V20. According to Tables II to V, it is easy to show that both the LF-case and the FL-case are the Nashsolutions to this game (for proof, see Appendix B). Here, we have the following proposition: LF

Proposition 1. In the hub-airport competition where each hub-airport can endogenously choose the role of Stackelberg leader or follower for the setting of the length of the connecting time, either the equilibrium where the hub-airport B acts as the leader and the hub-airport D acts as the follower (called Equilibrium LF), or the equilibrium where the hub-airport B acts as the follower and the hub-airport D acts as the leader (called Equilibrium FL) exists. In the LF equilibrium, we have the same qualitative results concerning the length of the connecting time and the total profits of each hub-airport as Lemma 1. However, the results in the FL equilibrium which are described in the following proposition may be interesting. Proposition 2-a. in the FL equilibrium, the hub-airport with a cost disadvantage in the provision of hub-airport service sets its connecting time shorter (longer) than its rival, when this cost disadvantage is small (sufficiently large). Proposition 2-b. in the FL equilibrium, even though the home country’s hub-airport bears a cost disadvantage in the provision of the airport service, the home country’s hub-airport does enjoy larger total profits than the neighbouring country’s hub-airport, when the cost disadvantage is not sufficiently large. Proof:

see Appendix C.

Propositions 2-a and 2-b can be intuitively explained as follows. In the FL-case, hub-airport B (acting as the Stackelberg follower) has room to adjust the length of its connecting time, and enjoys the ‘second mover advantage’ when the cost disadvantage is not sufficiently large. This result seems to correspond to the argument by Gal-or (1985) and Dowrick (1986). They demonstrate that when two ‘identical’ or ‘similar’ firms move sequentially in a game, the player that moves second (Stackelberg follower) earns higher profits than the player that moves first (leader) if the reaction functions of both players are upwards sloping. That is, second mover advantage exists. In our study, hub-airport B (bearing a cost disadvantage and acting as the follower) enjoys the second mover advantage as long as the difference of the costs is not sufficiently large21. 19

The concept of Stackelberg warfare has been discussed in, for example, Henderson and Quandt (1980, p. 207). It can be shown that the condition ∆θ < ∆1 (defined in footnote 15) is the sufficient condition for air-fares (and the demand of the connecting flight) are positive in the outcome for each case. 21 From equations (16) and (17), we directly know that the reaction function of both country’s hub-airports are upwards sloping. Further, it also can be confirmed that the isoprofit curves of each country is in the shape of a ‘U’, and higher isoprofit curves are associated with higher levels of profits. This explicitly implies, that lengthening the connecting time will increase the rival hub-airport’s total profits, i.e. the profits of the rival’s airline increase since the number of passengers increases and the air-fare rises, and also the concession profits of the rival hub-airport increase too since the number of passengers increases and the per passenger demand for concession goods is constant. 20


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Conclusion

This paper has highlighted the intensification of hub-airport competition that comes with the growth of hub-spoke airline networks. Given the fact that the concession revenue accounted for a high per cent of total revenue in many hub-airports and the plausibility that a hub-airport bearing a disadvantage in providing airport services may attempt to alleviate price competition, we have constructed a new network model where the hub-airports differentiate their own airport service by setting the length of the connecting time different from that of its rivals’ and by choosing the role of Stackelberg leader or follower for the connecting time setting, to maximise their total profits including the concession and aeronautical profits. Under the constructed network model, we have shown theoretically that if both countries’ hub-airports set the length of the connecting time simultaneously, the hub-airport with a disadvantage in providing the airport service obtains a smaller total profit than its rival hub-airport. However, if both countries’ hub-airports can endogenously choose the role of Stackelberg leader or follower for the connecting time setting, multiple Stackelberg equilibria exist. In the equilibrium where the home country’s hub-airport acts as the Stackelberg follower and it rival acts as the leader, even though the cost disadvantage exists, the home country’s hub-airport does obtain larger total profits than its rival when the cost disadvantage is not sufficiently large. A major contribution of this present paper to the literature is in developing a new hub-airport competition model. Even though a number of airport studies (Zhang and Zhang (1997), Zhang and Zhang (2003), Lu and Pagliari (2004), and Oum et al. (2004) are just a few recent examples) have discussed the socially optimal pricing and/or economic regulation issues based on a single airport modelling, little theoretical study deals with the issue of the increasing competition between multiple airports. Moreover, in the above studies, the behaviour of passengers has been treated as being reflected in the airlines’ demand for airport facilities. As a differentiation from the previous airport studies, this present paper has constructed a new model in which nonprice competition between two hub-airports, price competition between their major airlines, and the concession consumption of the transfer passengers in the hub-airport have been formulated. Further, the finding of this paper may provide a new methodology for the hub-airport (such as a major Japanese airport) that bears a cost disadvantage in the provision of airport services caused by geographical or technological reasons, and attempts to alleviate price competition. The analysis in this paper can be extended in a variety of ways. First, according to the general literatures on industry organisation, one firm might act as a leader and the other as follower by imposing an informational or psychological asymmetry, or more plausibly to regard asymmetry as the result of either a history or a threat of a dominant firm (e.g. Dowrick, 1986, p. 251). In our study, a hub-airport can act as a follower by observing its rival’s (major airline’s) timetable. A hub-airport might act as a leader, by collecting information for cognising its rival’s reaction to its own choice of the length of the connecting time. How a hub-airport can determine its rival’s reaction function should be an important part of future studies. Second, the non-price competition in the airline competition stage is considerable. For example, the analysis can be extended to the long-run one where airlines can choose the flight frequency. Then, the landing/ taking-off fee of hub-airports will have a direct effect on the flight frequency chosen by the airlines, and inevitably the setting of the connecting time will become complex. Also, the problem of congestion in the hub-airport should be considered in this kind of extension. Third, as Doganis (1992) indicated, promoting competition in the provision of concession goods may be a strategy for success in running the airport business. Thus, the supply side of the concession goods could be constructed in a different style and the different implications could be presented in future studies. © Blackwell Publishing Ltd / University of Adelaide and Flinders University 2006.

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Appendix A Table I

Bertrand-Nash equilibrium in the airline competition

α b (lB2 − lD2 ) A α b (lB2 − lD2 ) − , s2 = + 2 3 2 3

Air-fare

s1A =

Demand of connecting passengers

X 1A =

Gross profits of airlines

Π1A = s1A ⋅ X 1A , Π2A = s2A ⋅ X 2A

Table II

1 A A 1 A ⋅ s1 , X 2 = ⋅ s2 α α

FF equilibrium in the hub-airport competition stage

The length of the connecting time

lB2 =

3 − 16b 8[(6 − 16b )θ B + (3 − 16b )θ D ] α+ 2b 9 − 32b

lD2 =

3 − 16b 8[(3 − 16b )θ B + (6 − 16b )θ D ] α+ 2b 9 − 32b

FF

FF

Demand of concession goods (per passenger)

qBFF = lBFF /4 qDFF = lDFF /4

Air-fare

Demand of the connecting flight

s1FF =

1 8b (θ B − θ D ) α− 2 9 − 32b

s2FF =

1 8b (θ B − θ D ) α+ 2 9 − 32b

X 1FF = 1/α ⋅ s1FF X 2FF = 1/α ⋅ s2FF

Landing/taking-off fee

FBFF = θ B ⋅ X 1FF FDFF = θ D ⋅ X 2FF

Profits of airline

⎡1 ⎤ (9 − 24b ) 8b Π1FF = ⎢ α − θB + θ D ⎥ ⋅ X 1FF 2 ( 9 − 32 b ) ( 9 − 32 b ) ⎣ ⎦ ⎡1 8b (9 − 24b ) ⎤ Π2FF = ⎢ α + θB − θ D ⎥ ⋅ X 2FF 2 ( 9 − 32 b ) (9 − 32b ) ⎦ ⎣

Concession profits

⎡ (3 − 16b ) (6 − 16b ) (3 − 16b ) ⎤ Π BFF = ⎢ α+ θB + θ D ⎥ ⋅ X 1FF 16 9 32 9 − 32b ) ⎦ b ( − b ) ( ⎣ ⎡ (3 − 16b ) (3 − 16b ) (6 − 16b ) ⎤ θ D ⎥ ⋅ X 2FF Π DFF = ⎢ α+ θB + ( 9 − 32b ) ⎦ 16 b ( 9 − 32 b ) ⎣

Total profits

WBFF =

(3 − 8b ) 1 ⋅ ⋅ [(9 − 32b )α − 16b(θ B − θ D )]2 α 32b(9 − 32b )2

WDFF =

(3 − 8b ) 1 ⋅ ⋅ [(9 − 32b )α + 16b(θ B − θ D )]2 α 32b(9 − 32b )2


312 Table III


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LF outcome in the hub-airport competition stage


lB2 =

(3 − 16b )(9 − 32b ) 4 (3 − 8b ) 4 (3 − 16b ) α+ θB + θD 12b(1 − 4b ) 3(1 − 4b ) 3(1 − 4b )

lD2 =

2 (9 − 32b ) (3 − 16b )(15 − 64b ) 2 (3 − 16b ) θB + θD α+ 3(1 − 4b ) 3(1 − 4b ) 24b (1 − 4b )

LF

LF


qBLF = lBLF /4

Air-fare

s1LF =

(9 − 32b ) 2b α− (θ B − θ D ) 24(1 − 4b ) 3(1 − 4b )

s2LF =

(15 − 64b ) 2b α+ (θ B − θ D ) 24(1 − 4b ) 3(1 − 4b )


qDLF = lDLF /4

X 1LF = 1/α ⋅ s1LF X 2LF = 1/α ⋅ s2LF


FBLF = θ B ⋅ X 1LF FDLF = θ D ⋅ X 2LF

Profits of airline

⎡ (9 − 32b ) ⎤ (3 − 10b ) 2b Π1LF = ⎢ α− θB + θ D ⎥ ⋅ X 1LF 3(1 − 4b ) 3(1 − 4b ) ⎦ ⎣ 24(1 − 4b ) ⎡ (15 − 64b ) (3 − 10b ) ⎤ LF 2b θD ⎥ ⋅ X 2 Π2LF = ⎢ α+ θB − ( − ) ( − ) 3(1 − 4b ) ⎦ 24 1 4 b 3 1 4 b ⎣

Concession profits

⎡ (3 − 16b )(9 − 32b ) (3 − 8b ) (3 − 16b ) ⎤ LF Π LF α+ θB + θD ⎥ ⋅ X1 B = ⎢ 96 1 − 4 6 1 − 4 6(1 − 4b ) ⎦ b ( b ) ( b ) ⎣ ⎡ (3 − 16b )(15 − 64b ) (3 − 16b ) (9 − 32b ) ⎤ LF α+ θB + θD ⎥ ⋅ X 2 Π LF D = ⎢ 192 ( 1 − 4 12 1 − 4 12 ) ( ) (1 − 4b ) ⎦ b b b ⎣

Total profits

WBLF =

1 1 ⋅ ⋅ [(9 − 32b )α − 16b(θ B − θ D )]2 α 768b(1 − 4b )

WDLF =

1 (3 − 8b ) ⋅ ⋅ [(15 − 64b )α + 16b(θ B − θ D )]2 α 4608b (1 − 4b )2


2006 Table IV


313

FL outcome in the hub-airport competition stage


lB2 =

(3 − 16b )(15 − 64b ) 2(9 − 32b ) 2(3 − 16b ) α+ θB + θD 24b(1 − 4b ) 3(1 − 4b ) 3(1 − 4b )

lD2 =

4(3 − 8b ) (3 − 16b )(9 − 32b ) 4(3 − 16b ) θB + θD α+ 3(1 − 4b ) 3(1 − 4b ) 12b(1 − 4b )

FL

FL


qBFL = lBFL /4

Air-fare

s1FL =

(15 − 64b ) 2b α− (θ B − θ D ) 24(1 − 4b ) 3(1 − 4b )

s2FL =

(9 − 32b ) 2b α+ (θ B − θ D ) 24(1 − 4b ) 3(1 − 4b )


qDFL = lDFL /4

X 1FL = 1/α ⋅ s1FL X 2FL = 1/α ⋅ s2FL


FBFL = θ B ⋅ X 1FL FDFL = θ D ⋅ X 2FL

Profits of airline

⎡ (15 − 64b ) ⎤ (3 − 10b ) 2b Π1FL = ⎢ α− θB + θ D ⎥ ⋅ X 1FL 24 ( 1 − 4 b ) 3 ( 1 − 4 b ) 3 ( 1 − 4 b ) ⎣ ⎦ ⎡ (9 − 32b ) (3 − 10b ) ⎤ FL 2b θD ⎥ ⋅ X 2 Π2FL = ⎢ α+ θB − ( ) ( ) 3(1 − 4b ) ⎦ 24 1 − 4 b 3 1 − 4 b ⎣

Concession profits

⎡ (3 − 16b )(15 − 64b ) (9 − 32b ) (3 − 16b ) ⎤ FL Π BFL = ⎢ α+ θB + θD ⎥ ⋅ X1 192 1 4 12 1 4 12 (1 − 4b ) ⎦ b ( − b ) ( − b ) ⎣ ⎡ (3 − 16b )(9 − 32b ) (3 − 16b ) (3 − 8b ) ⎤ FL θB + θD ⎥ ⋅ X 2 Π DFL = ⎢ α+ 96 ( 1 4 ) 6 ( 1 − 4 ) 6 (1 − 4b ) ⎦ b b − b ⎣

Total profits

WBFL =

(3 − 8b ) 1 ⋅ ⋅ [(15 − 64b )α − 16b(θ B − θ D )]2 α 4608b(1 − 4b )2

WDFL =

1 1 ⋅ ⋅ [(9 − 32b )α + 16b(θ B − θ D )]2 α 768b(1 − 4b )


314 Table V


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LL outcome in the hub-airport competition stage


lB2 =

(3 − 16b )(9 − 32b ) 4(3 − 8b ) 4(3 − 16b ) α+ θB + θD 12b(1 − 4b ) 3(1 − 4b ) 3(1 − 4b )

lD2 =

4(3 − 8b ) (3 − 16b )(9 − 32b ) 4(3 − 16b ) θB + θD α+ 3(1 − 4b ) 3(1 − 4b ) 12b(1 − 4b )

LL

LL


Air-fare

qBLL = lBLL /4 qDLL = lDLL /4 1 32b2 s1LL = α − (θ B − θ D ) 2 9(1 − 4b ) 1 32b2 s2LL = α + (θ B − θ D ) 2 9(1 − 4b )


X 1LL = 1/α ⋅ s1LL X 2LL = 1/α ⋅ s2LL


FBLL = θ B ⋅ X 1LL FDLL = θ D ⋅ X 2LL

Profits of airline

⎡1 ⎤ (3 − 8b )(3 − 4b ) 32b2 Π1LL = ⎢ α − θB + θ D ⎥ ⋅ X 1LL 9(1 − 4b ) 9(1 − 4b ) ⎥⎦ ⎢⎣ 2 ⎡1 32b2 (3 − 8b )(3 − 4b ) ⎤ LL θD ⎥ ⋅ X 2 Π2LL = ⎢ α + θB − 9(1 − 4b ) 9(1 − 4b ) ⎢⎣ 2 ⎥⎦

Concession profits

⎡ (3 − 16b )(9 − 32b ) (3 − 8b ) (3 − 16b ) ⎤ LL Π LL α+ θB + θD ⎥ ⋅ X1 B = ⎢ − 96 b ( 1 – 4 ) 6 ( 1 4 b ) 6(1 − 4b ) ⎦ ⎣ ⎡ (3 − 16b )(9 − 32b ) (3 − 16b ) (3 − 8b ) ⎤ LL θB + θD ⎥ ⋅ X 2 Π LL α+ D = ⎢ 6(1 − 4b ) 6(1 − 4b ) ⎦ 96b(1 – 4 ) ⎣

Total profits

WBLL =

1 (3 − 8b ) ⋅ × α 6(1 − 4b )

⎤ ⎡ 9 − 40b 2 (9 − 24b − 64b2 ) (3 − 8b )32b2 α − (θ B − θ D )α + (θ B − θ D )2 ⎥ ⎢ 18(1 − 4b ) 27(1 − 4b ) ⎥⎦ ⎢⎣ 32b WDLL =

1 (3 − 8b ) ⋅ × α 6(1 − 4b )

⎤ ⎡ 9 − 40b 2 (9 − 24b − 64b2 ) (3 − 8b )32b2 α + (θ B − θ D )α + (θ B − θ D )2 ⎥ ⎢ b ( − b ) ( − b ) 32 18 1 4 27 1 4 ⎥⎦ ⎢⎣


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Appendix B According to Tables II to V we have the following results of the outcome comparison. WBLF − WBFF =

1 (3 − 16b)2 ⋅ ⋅ [(9 − 32b)α − 16b(θ B − θ D )]2 > 0 α 768b(1 − 4b)(9 − 32b)2

(B-1)

WBFL − WBLL =

(3 − 16b)2 1 ⋅ ⋅ [3α − 16b(θ B − θ D )]2 > 0 α 6912b(1 − 4b)

(B-2)

WDLF − WDLL =

1 (3 − 16b)2 ⋅ ⋅ [(9 − 32b)α + 16b(θ B − θ D )]2 > 0 α 768b(1 − 4b)(9 − 32b)2

(B -3)

WDFL − WDFF =

(3 − 16b)2 1 ⋅ ⋅ [3α + 16b(θ B − θ D )]2 > 0 α 6912b(1 − 4b)

(B -4)

Thus, both LF-case and FL-case are the Nash-solutions to the role-choosing game.

Appendix C Proof for proposition 2-a: From Table III we have lB2 − lD2 = − FL

FL

⎡ 3 − 16b ⎤ 1 ⋅⎢ ⋅ α − 2(θ B − θ D )⎥ (1 − 4b) ⎣ 8b ⎦

(C-1)

The condition for equation (C-1) is positive is (θB − θD) ≡ ∆θ > (3 − 16b)α/16b ≡ ∆9. Recall that the positive condition for air-fare is (θB − θD) ≡ ∆θ < (9 − 32b)α/16b ≡ ∆1. Thus, lB2 < lD2 , for (0 < ∆θ < ∆9) and lB2 ≥ lD2 , for (∆9 ≤ ∆θ < ∆1). FL

FL

FL

FL

Proof for Proposition 2-b: From Table III we have WDFL − WBFL =

1 1 ⋅ ⋅ [ L ⋅ ( ∆θ )2 + Mα ⋅ ∆θ − Nα 2 ] α 4608b(1 − 4b)2

(C-2)

where L ≡ 256b2(3 − 16b) > 0 M ≡ 32b(9 − 72b + 128b2) > 0 G ≡ (3 − 16b)(63 − 384b + 512b2) > 0 The condition for equation (C-2) is negative is ∆θ ≤ α[( −M + M 2 + 4LN )/2L ] ≡ ∆θW . It can be numerically shown that ∆θW < ∆1 for any b < 3/16. Recall that the positive condition for air-fare is (θB − θD ) ≡ ∆θ < (9 − 32b)α/16b ≡ ∆1. Thus, WDFL < WBFL , for (0 < ∆θ < ∆θW)

and WDFL ≥ WBFL , for (∆θW ≤ ∆θ < ∆1)


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References Anderson, S. 1987, ‘Spatial Competition and Price Leadership’, International Journal of Industrial Organization, vol. 5, pp. 369 – 398. Bittlingmayer, G. 1990, ‘Efficiency and Entry in a Simple Airline Network’, International Journal of Industrial Organization, vol. 8, pp. 245 –257. Borenstein, S. and Netz, J. 1999, ‘Why Do All the Flights Leave at 8 am? Competition and Departuretime Differentiation in Airline Markets’, International Journal of Industrial Organization, vol. 17, pp. 611– 640. Brucekner, J.K. and Whalen, W.T. 2000, ‘The Price Effects of International Airline Alliances’, Journal of Law and Economics, vol. 53, pp. 503 – 545. Brueckner, J. and Spiller, P. 1991, ‘Competition and Mergers in Airline Networks’, International Journal of Industrial Organization, vol. 9, pp. 323 – 342. Bruinsma, F., Rietveld, P. and Brons, M. 2000, ‘Comparative Study of Hub Airports in Europe: Ticket Prices, Travel Time and Rescheduling Costs’, Journal of Economic and Social Geography, vol. 91, pp. 278– 292. De Vany, A.S. 1974, ‘The Revealed Value of Time in Air Travel’, Review of Economics and Statistics, vol. 56, pp. 77– 82. Doganis, R. 1992, The Airport Business, Routledge. Dowrick, S. 1986, ‘Von Stackelberg and Cournot Duopoly: Choosing Roles’, Rand Journal of Economics, vol. 17, pp. 251– 260. Encaoua, D., Moreaux M. and Perrot A. 1996, ‘Compatibility and Competition in Airline: Demand Side Network Effects’, International Journal of Industrial Organization, vol. 14, pp. 701–726. Furth, D. and Kovenock, D. 1993, ‘Price Leadership in a Duopoly with Capacity Constraints and Product Differentiation’, Journal of Economics, vol. pp. 57, 1– 35. Gal-or, E. 1985, ‘First Mover and Second Mover Advantages’, International Economics Review, vol. 26, pp. 649– 653. Hanlon, P. 1999, Global Airlines: Competition in a Transnational Industry, second edition, ButterworthHeinemann Ltd. Henderson, J.M. and Quandt, R.E. 1980, Microeconomic Theory: A Mathematical Approach, third edition, McGraw-Hill, Singapore. Hendricks, K., Piccione, M. and Tan, G. 1995, ‘The Economics of Hubs: the Case of Monopoly’, Review of Economic Studies, vol. 62, pp. 83 – 99. ——, —— and —— 1997, ‘Entry and Exit in Hub-spoke Networks’, Rand Journal of Economics, vol. 28, pp. 291– 303. Hotelling, H. 1929, ‘Stability in Competition’, Economic Journal, vol. 39, pp. 41–57. Hsu, C.I. and Chao, C.C. 2005, ‘Space Allocation for Commercial Activities at International Passenger Terminals’, Transportation Research Part E, vol. 41, pp. 29 – 51. Jones, I., Viehoff, I. and Marks, P. 1993, ‘The Economics of Airport Slots’, Fiscal Studies, vol. 14, no. 4, pp. 37– 57. Kuroda, T. and Yagi, T. 1999, ‘International Airport War: a Game Theoretic Approach for Financial Scheme of Hub Airports’, SIS/GSHI Discussion Paper, no. 99-2. Langner, J. 1996, ‘The Allocation of Slots in the Airline Industry, Nomos. Lin, M.H. 2003, ‘Hub-airport Competition, Airline Competition and Economic Welfare’, Economic Science, vol. 50, no. 4, pp. 49 – 65. —— 2004, ‘Strategic Airline Alliances and Endogenous Stackelberg Equilibria’, Transportation Research Part E, vol. 40, pp. 357– 384. Lu, C.C. and Pagliari, R.I. 2004, ‘Evaluating the Potential Impact of Alternative Airport Pricing Approaches on Social Welfare’, Transportation Research Part E, vol. 40, pp. 1–17. Oum, T.H., Zhang, A. and Zhang, Y. 1995, ‘Airline Network Rivalry’, Canadian Journal of Economics, vol. 28, pp. 836– 857. ——, —— and —— 2004, ‘Alternative Forms of Economic Regulation and Their Efficiency Implications for Airports’, Journal of Transport Economics and Policy, vol. 38, pp. 217–246. Panzer, J.C. 1979, ‘Equilibrium and Welfare in Unregulated Airline Markets’, American Economic Review, vol. 69, pp. 92 – 95. © Blackwell Publishing Ltd / University of Adelaide and Flinders University 2006.

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Park, J.H. 1997, ‘The Effect of Airline Alliances on Markets and Economic Welfare’, Transportation Research Part E, vol. 33, pp. 181–195. Pels, Nijkamp, P. and Rietveld, P. 1997, ‘Subtitution and Complementarity in Aviation: Airports vs Airlines’, Transportation Research Part E, vol. 33, pp. 275 –286. Prescott, E.C. and Visscher, M. 1977, ‘Sequential Location among Firms with Foresight’, Bell Journal of Economics, vol. 8, pp. 378 – 393. Rietveld, P. and Brons, M. 2001, ‘Quality of Hub-and-spoke Networks; the Effects of Timetable Co-ordination on Waiting Time and Rescheduling Time’, Journal of Air Transport Management, vol. 7, pp. 241– 249. Salvanes, K.G., Steen, F. and Sorgard, L. 2005, ‘Hotelling in the Air? Flight Departures in Norway’, Regional Science and Urban Economics, vol. 35, pp. 193 –213. Spiller, P.T. 1989, ‘A Note on Pricing of Hub and Spoke Networks’, Economics Letters, vol. 30, pp. 165 –169. Teraoka, Y., Osumi, S. and Hohjo. H. 2003, ‘Some Stackelberg Type Location Game’, Computers and Mathematics with Applications, vol. 46, pp. 1147 –1154. Tirole, J. 1988, The Theory of Industrial Organization, MIT Press, Cambridge, MA. Zhang, A. 1996, ‘An Analysis of Fortress Hubs in Airline Networks’, Journal of Transport Economics and Policy, vol. 30, pp. 293 – 307. —— and Zhang, Y. 1997, ‘Concession Revenue and Optimal Airport Pricing’, Transportation Research Part E, vol. 33, pp. 287–296. —— and —— 2003, ‘Airport Charges and Capacity Expansion: Effects of Concessions and Privatization’, Journal of Urban Economics, vol. 53, pp. 54 –75. —— and Wei, X. 1993, ‘Competition in Airline Networks: The Case of Constant Elasticity Demands’, Economics Letters, vol. 42, pp. 253 –259.
