An Interpretative Survey of Analytical Models of Airport Pricing

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06 07 4 08

10 An Interpretative Survey of Analytical Models ∗ 11 of Airport Pricing 12

13 † ‡ 14 Leonardo J. Basso and Anming Zhang 15

20 21 ABSTRACT 22 In this chapter, we review analytical models of airport pricing, from 1987 onward. We 23 argue that articles in the literature can be grouped into two approaches, the traditional 24 approach and the vertical structure approach. In the traditional approach, the demand for 25 airports depends on airport charges and on congestion costs of both passengers and airlines; 26 the airline market is not formally modeled under the assumption that airline competition 27 is perfect. In the vertical structure approach, airports are recognized as providing an input 28 for the airline market, which is modeled as an oligopoly where firms have market power.

29 It is the equilibrium of this downstream market that determines the airports’ demand: the

30 demand for airports is thus derived demand. We present and discuss both approaches and the papers within each of them, highlighting how they have analyzed different aspects of airport 31 pricing such as the efficiency of weight-based airport charges, the effects of concession 32 revenues on pricing and capacity investments, or the effects of airlines’ market power on 33 optimal runway congestion pricing. We study the connection between the approaches and 34 the transferability of results, and also discuss a handful of articles that have looked at the 35 pricing of airport networks, i.e., three or more connected airports, as opposed to airports in 36 isolation. We conclude by providing what we think should be the lines of future research. 37

39 ∗ Acknowledgement: We would like to thank Darin Lee and Monica Hartmann for helpful comments. Finan- 40 cial support from the Social Science and Humanities Research Council of Canada (SSHRC) is gratefully 41 acknowledged. † 42 Corresponding author. Sauder School of Business, The University of British Columbia. Department of Civil

43 Engineering, Universidad de Chile. Contact information: 2053 Main Mall, Vancouver BC, Canada V6T 1Z2, Tel.: 1-604 822 0288, Fax: 1-604 822 9574, [email protected]/Casilla 228-3, Santiago, Chile, Tel.: 56-2 44 978 4380, Fax: 56-2 689 4206, [email protected]. 45 ‡ Sauder School of Business, The University of British Columbia. Contact information: 2053 Main Mall, 46 Vancouver BC, Canada V6T 1Z2, Tel.: 1-604 822 8420, Fax: 1-604 822 9574, [email protected].

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90 LEONARDO J. BASSO AND ANMING ZHANG

01 1 INTRODUCTION 02 03 Airport pricing has attracted the attention of economists for some time now, starting with 04 Levine (1969) and Carlin and Park (1970). Most of the attention has been devoted to the 05 efficiency of pricing practices by airport authorities and the need to take into account 06 congestion which, even in the early 1970s, was afflicting passengers and airlines. The 07 alleged inefficiencies of actual pricing practices plus the increase in delays at airports 08 around the world have made understanding the models of airport pricing very germane 09 in today’s world. Airport delays in the United States have grown dramatically in recent 10 years. In 2004, 20 per cent of flights arrived more than 15 min late, with Chicago’s 11 O’Hare airport being last with 30 per cent. The US Department of Transportation in its 12 “National Strategy to Reduce Congestion on America’s Transportation Network” (2006) 13 has estimated that aircraft delays cost passengers $9.4 billion. Congestion is perhaps 14 even more acute at some of the major European, Japanese, and Chinese airports. 15 Furthermore, the recent trend of airport privatization and/or commercialization 16 induced, in addition, a focus on the effects of privatization and the efficiency of different 17 regulatory schemes (this trend started in the late 1980s throughout the world following 18 the examples in the United Kingdom). More specifically, privatized airports would pur- 19 sue maximization of profits. On the other hand, it has usually been accepted that airports 20 enjoy a local monopoly position because they have a captive market. Besides, sizeable 21 economies of scale on airport infrastructure provision and airport operations may exist 22 (Doganis, 1992). Out of the concern that private airports would exert market power 23 in user charges, many private (and public) airports are under some type of economic 24 regulation such as rate-of-return or price caps. 25 The work on airport pricing has been considerable. Some old questions, such as how 26 we should use the price mechanism to signal congestion problems, have persisted in the 27 literature. New questions, such as whether privatization would induce better capacity 28 investment, have appeared. As far as we know, there has been no paper that is devoted 29 to putting together all the questions and answers that have been obtained in the literature 30 since the late 1980s. We attempt to do that in this chapter. Specifically, we review the 31 airport pricing literature, with a focus on analytical papers. Indeed, we are narrowing the 32 scope of our work, by leaving aside a number of important empirical papers. By this we 33 do not mean that the empirical work is irrelevant, but as it will be seen, a comprehensive 34 survey of the analytics of airport pricing easily use up the space in a paper, and we 35 believe that a good command of theoretical and analytic results helps to better grasp 36 empirical findings. Also, we will focus on papers in the last 20 years. We believe that 37 this is enough to understand what is known today about the theory of airport pricing, 38 since earlier contributions such as Levine (1969), Carlin and Park (1970), and Morrison 39 (1983) have been incorporated into the papers we will review. While there are many 40 survey papers on airlines, the survey work on airports is relatively rare. One exception 41 is a recent survey paper by Forsyth (2000), in which he focused mainly on the pre-1990 42 airport-pricing papers and on models of airport costs and production efficiency. 43 We shall summarize the findings and provide directions of what we think should 44 be future research. In order to do this in an orderly manner, we group the papers into 45 two broad “approaches”. Papers within one approach share many features regarding the 46 analytical modeling, which makes it easier to explain what characterize them, while

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INTERPRETATIVE SURVEY OF ANALYTICAL MODELS 91

01 also enabling a better description of the contributions of each of the individual articles. 02 Therefore, Sections 2 and 3 will be devoted to explain what we have called “the tra- 03 ditional approach” and “the vertical structure approach” to airport pricing respectively 04 and, within each approach, what we have learned from individual articles. Because an 05 obvious question is whether results from one approach can be transferred to the other, in 06 Section 4 we discuss connections between the approaches as a means to better understand 07 how the results stemming from the two approaches relate to each other. 08 In what follows, Sections 2 and 3 deal with a single airport’s decision or, at most, 09 two (complementary) airports, given the complexity of the economics of airport pricing. 10 However, there are a handful of articles that have looked at the pricing of airport 11 networks, i.e., three or more connected airports. We discuss these papers in Section 5, 12 noting that the previous classification may still be applied. We conclude in Section 6 by 13 providing what we think should be the lines of future research. 14

15 16 2 THE TRADITIONAL APPROACH TO AIRPORT PRICING 17 18 The main characteristic of the traditional approach is that it typically follows a “partial 19 equilibrium” analysis in which an airport’s demand is directly a function of the airport’s 20 own decisions. As will be explained below, since airlines’ decisions (and airline com- 21 petition) are not directly considered, the derived characteristic of the airport’s demand 22 is not formally recognized. In this section, we consider papers by Morrison (1987), 23 Morrison and Winston (1989), Oum and Zhang (1990), Zhang and Zhang (1997, 2001, 24 2003), Carlsson (2003), Oum et al. (2004), Lu and Pagliari (2004), and Czerny (2006). 25 Most of these papers follow essentially the same model: the demand for an airport is 26 assumed to be a function of a “full price”. This full price includes the airport charge and, 27 in an additive fashion, some cost measure of the delays caused by congestion. Delay 28 functions have always been measured through some non-linear function of traffic and 29 capacity, although the modeling has not been unique: the main discrepancy has been 30 whether the function should (or not) be homogenous of degree one in the traffic to 31 capacity ratio. Delay is assumed to affect both airlines and passengers, and consumers’ 32 surplus is measured by integration of the airport’s demand. When the airport capacity 33 is variable, the cost function has been usually assumed to be separable in operating and 34 capacity costs. 35 This approach has been used to analyze a variety of issues regarding airport pricing 36 and capacity decisions and under many different sets of assumption, as can be seen 37 in Table 1. Initially, the focus was on deriving optimal prices and capacities in the 38 presence of congestion but, lately, it has been used to assess the effects of privatization 39 and regulation as well. 40 The basics of the traditional approach may be synthesized in a fairly concise analytical 41 manner, which we present below.1 In order to provide aviation services, an airport 42

44 1 Certainly, not all the papers can directly be assimilated to this presentation – particularly Lu and Pagliari 45 (2004) and Czerny (2006) may seem more distant – but most of them fit through some adjustments, which 46 will be indicated where relevant.

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08 operations. added to SW 09 demands. incorporating concessions They include concession BC is in the long run Social cost of emissions First model to formally demands dependent demands independent demands 10 independent demands

12 NHDO One period. NHDO One period. NHDO Many periods, independent NHDO Many periods with 13 HDO Many periods with

18 Variable and lumpy continuous continuous lumpy continuous 19

26 (from 1987 on)

27 case) Max SW Max profits (private Max SW st BC Max SW st BCMax SW Lumpy NHDO Many periods, independent Variable and Max SW st BC Variable and Max SW Variable and Max SW st BCMax SW Fixed NHDO Variable and Many periods with 28

33 Traditional Approach

38 lumpy Analyze privatization and the effects of concessions on pricing and capacities Analyze whether public airport should have a strictbrake-even (short constraint run) or a longer run constraint with congestion and emissions Effects of concessions. Should the BC be commonconcessions to and both airside activities or separate? Analyze budget adequacy under congestion pricing when capacity investments are regulators give to eachaircraft type when of they max SW Efficient pricing and capacity with congestion 39

42 Summary of Papers Using the 43

45 Zhang and Zhang (2003) Zhang and Zhang (2001) Carlsson (2003) Efficient pricing and capacity Zhang and Zhang (1997) Oum and Zhang (1990) Table 1 AuthorMorrison (1987) Uncover the importance Morrison and Goal of theWinston Paper (1989) Objective Functions Capacity Delay Observations 46

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03 nction

10 operations. charges determine the number of consumers. They include concession BC is in the long run 11 they assumed that capacity is a restriction onoutput: feasible potential for excess demand

15 No delays Both airside and concession NHDO One period. 16

21 Fixed but large: no excess demand Variable and continuous Fixed No delays Rather than having delays, 22

27 Max SW Max Profits st two different forms of regulation Max SW st BC Max profits (private case) Max profits st four different forms of regulation 28 Max profits st two different forms of regulation

39 on aeronautical charges. Regulation: single-till versus dual-till cap Efficiency implications of alternative forms of regulation Regulation and concessions: single-till versus dual-till cap 40

45 Czerny (2006) Effects of concessions Oum, et al. (2004) Lu and Pagliari (2004) SW: social welfare; BC:is budget homogenous constraint; of degree NHDO: one the in delay the function traffic is to non-homogenous capacity ratio. of degree one in the traffic to capacity ratio; HDO: the delay fu 46

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94 LEONARDO J. BASSO AND ANMING ZHANG

01 incurs both operating and capital expenses. It collects user charges to cover these costs 02 and, in the private-airport case, to make a return on capital investments. For a given 03 capacity, congestion will start to build up at the airport as demand grows, inducing 04 delays and therefore extra costs on passengers and airlines. It is usually assumed that 05 airlines fully pass airport charges to passengers; the same is assumed for airlines delay 2 06 costs. Therefore, passengers will perceive a full price consisting of the airport charge, 07 the flight delay cost, travel-time costs plus other airline charges (e.g., air ticket). It 08 has been argued that since other airline charges are exogenous as far as the airport is 09 concerned, the demand an airport faces may be considered to be a function only of the 10 airport charge P and the flight delay cost D, which includes the delay costs to both 3 11 airlines and passengers. The variables in the model would be 12 13 Q Demand for airport facilities measured by the number of flights, which is a function 14 of the full price perceived by passengers 15 = P + D the full price that determines the airport’s demand 16 P airport charge per flight 17 D = DQ K flight delay cost experienced by each flight, which depends on traffic Q 18 and airport capacity K 19 K capacity of the airport 20 CQ operating costs of the airport 21 r cost of capital.

22 23 The capacity may be lumpy or continuously adjustable. The assumption of adjustable 24 capacity has been justified based on the observation that capacity would be defined not 25 only by the number of runways – which can only be increased discretely – but also by

26 air traffic control technology, air navigation systems and other infrastructures, which

27 can be increased or enhanced continuously.

28 One of the first issues that was analyzed using the traditional approach is the nature

29 of the airport’s choices of user charge P and capacity K, for the benchmark case in

30 which social welfare is maximized subject to a budget constraint – the public airport

31 case. The problem the public airport faces is given by 32 33 max Qd + PQ − CQ − rK (1) 34 PtK 35

36 37 stPQ − CQ − rK = 0(2) 38

39 40 2 Morrison (1987, p. 48) makes this assumption by equating the airlines’ elasticity of demand for airport 41 services to the elasticity of passengers’ demand with respect to full price times the fraction that airport charges 42 and congestion costs represent in total flight costs (see also Raffarin, 2004, p. 115). Oum et al. (2004) make

43 this assumption explicitly, arguing that this will be the case under perfect competition. 3 Here, for notational simplicity, we present a model with no intraday variations in demand, i.e., a “single 44 period” model. The model can be extended in a straightforward fashion to the case of many periods so long 45 as the demands in these periods are independent. The independence assumption has been made in most papers 46 that deal with multiple periods; the only exception is Oum and Zhang (1990).

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01 The first term in the objective function would correspond to consumer surplus, the 02 remaining terms are the airport’s profit. Forming the Lagrangean and taking derivatives 03 with respect to P and K, first-order conditions are obtained. From them, the following 04 pricing and capacity investment rules follow: 05 D 06 P = C + Q + (3) Q 1 + 07

08 D 09 −Q = r (4) 10 K 11 where denotes the Lagrange multiplier of the budget constraint, and is the (positive) 12 elasticity of demand with respect to the full price. According to Morrison (1987) and 13 Zhang and Zhang (1997, 2001), the interpretation of the pricing rule is as follows: 14 The first two terms on the right-hand side (RHS) of Equation (3) represent the social 15 marginal cost (SMC) of one flight (operational marginal cost plus the marginal cost of 16 congestion), whereas the third term represents a markup that is inversely related to and 17 depends on the severity of the budget constraint. Hence, the difference with the usual 18 Ramsey-Boiteux pricing is that the pricing rule needs to take into account the congestion 19 that a new flight imposes on others. 20 Regarding the optimal capacity rule – Equation (4) – Zhang and Zhang (1997) note 21 that it does not depend on and hence it is identical to the one obtained when a 22 budget constraint is not imposed, as in Morrison and Winston (1989). Therefore, airport 23 authorities that adopt Ramsey pricing should still pursue the same optimal policy of 24 capacity investment. In this policy, the socially optimal level of capacity is set such that 25 the marginal benefit of capacity in terms of reduction in delays, equates the marginal 26 cost of capacity (Morrison and Winston, 1989; Zhang and Zhang, 1997). 27 This concludes the explanation of the basic setup of the approach. In what follows 28 then, we will look at how this approach has been used – and modified when needed – 29 to analyze issues other than second best pricing and capacity investment. Authors 30 have used the traditional approach to (i) study the efficiency of weight-based airport 31 charges, (ii) analyze the effects that lumpy investments in capacity may have on bud- 32 get adequacy, (iii) examine the effects of concession revenues on pricing and capacity 33 investments, (iv) derive efficiency implications of alternative forms of regulation, and 34 (v) study how environmental cots could be incorporated into airports’ charges. 35 36 2.1 On Weight-Based Airport Charges 37

38 Because in general, aircraft are not charged by the contribution they make to congestion

39 but by their weight, Morrison (1987) wanted to uncover the importance regulators give

40 to each type of aircraft when choosing the runway landing fees. For this, he assumed

41 that the demand is Qi, where i denotes a class of airport users, that is, different types of

42 aircraft. Then, assuming that capacity is fixed, he put weights on the contribution of each

43 class of users to the social-welfare function. Hence, the objective function (1) becomes 44 + − 45 i Qiidi PiQi CQi (5) i 46

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96 LEONARDO J. BASSO AND ANMING ZHANG

01 where i is the weight of user i. With this social-welfare function, and still considering 02 the budget constraint in Equation (2), the optimal pricing rule Equation (3) changes to 03 D + 1 − 04 P = C + Q + i i i i + (6) 05 Qi 1 i 06 Morrison then asked the following question: what set of weights is implied by actual 07 airport charges? To uncover the weights, he followed Ross (1984) and solved for the 08 weights i in Equation (6). Using actual data, those weights can be obtained up to a 09 multiplicative constant. Morrison’s main result was that when the airport is uncongested, 10 weight-based landing fees imply welfare weights (the i) that are very similar. But 11 when congestion increases, the dispersion in the weights also increases, implying that 12 the weight-based landing fees would be less appropriate when there is congestion. He 13 argued that this happens because, though weight is a reasonable proxy for elasticity of 14 demand, it is a poor proxy for congestion costs. 15

18 2.2 Lumpy Capacity and Cost Recovery 19 Oum and Zhang (1990) and Zhang and Zhang (2001) were interested in how budget 20 adequacy would be affected if capacity can be increased only in discrete lumps. The 21 conjecture was that the lumpy nature of capacity expansions would make social marginal 22 congestion pricing lead to alternating periods of airport surplus and deficits. Oum and 23 Zhang (1990) incorporated a positive time trend to the airport’s demand to capture the 24 fact that the aviation demand would increase with the overall economy. By considering 25 lumpy capacity expansions – that is, K can be increased only by a minimum amount K – 26 they focused on the timing of capacity expansions rather than the capacity investment 27 in a steady state as discussed above (budget constraint was not considered, however). 28 They concluded that, when capacity is indivisible, the optimal congestion pricing – 29 given by Equation (3) with = 0 – and optimal capacity expansion would lead to 30 alternating periods of excess capacity and capacity shortage. During capacity shortage, 31 the congestion toll would exceed annualized capacity costs but during excess capacity, 32 the congestion toll would fall short of annualized capacity costs. This implies that budget 33 adequacy would depend entirely on the number of shortage/excess capacity periods 34 between capacity expansions. And the number of periods in each case depends on the 35 pattern of traffic growth. 36 Oum and Zhang (1990) concluded that when capacity is indivisible, the cost recovery 37 status of an airport cannot be predicted without reference to the time path of the 38 traffic growth and, therefore, the cost recovery theorem for investment in transportation 39 infrastructure would not hold. This important theorem states that (see, e.g., Mohring, 40 1976) when operational costs are separable from capacity costs, the latter exhibit constant 41 returns to scale, and the delay function is homogenous of degree one in the traffic to 42 capacity ratio, optimal congestion pricing and capacity provision leads to exact cost 43 recovery of capacity investments and operational costs. This is not the only way in which 44 the cost recovery theorem would fail for airports though. Even if capacity is divisible, 45 as in the basic model shown in Equations (1) and (2), Zhang and Zhang (1997) showed 46 that, without a budget constraint, social-marginal-cost pricing would always give rise to

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01 a financial deficit to the airport because the delay function D would not be homogenous 02 of degree one in the traffic to capacity ratio (Lave and De Salvo, 1968; US Federal 03 Aviation Administration, 1969; see Horonjeff and McKelvey, 1983). Furthermore, the 04 deficit would increase with the congested airport. 05 Given all this, Zhang and Zhang (2001) were interested in the case where delays 06 are non-homogenous of degree one, capacity is indivisible, traffic grows over time, but 07 airports are required to recover their costs from both operations and capacity investments. 08 The question they asked was – Should public airports be asked to break even in the short 09 run, or in the long run, which may involve taking losses in early years of a capacity 10 investment but surplus in later years? For this, they modified the airport’s problem 11 (1)–(2), so as to consider that the airport would now maximize social welfare over a 12 period of time S, while achieving cost recovery over the entire period. Capacity was 13 assumed to be fixed during the period, owing to its indivisibility. The new long-run 14 problem faced by the public airport is 15

16 S 17 max Q sd + PQ − CQ − rK e−rsds P K 18 t 0 19 (7) S 20 st PQ s − CQ − rKe−rsds = 0 21 0 22 23 Now, the airport’s demand increases with time, that is, Q/s > 0, and future revenues 24 are discounted using the cost of capital, r. The short-run problem is as in Equations 25 (1)–(2). Not surprisingly, Zhang and Zhang found that the short-run financial break-even 26 constraint leads to a lower level of social welfare than a long-run break-even constraint. 27 This increase in welfare is expected, since short-run budget adequacy implies long-run 28 budget adequacy but not vice versa. In fact, Zhang and Zhang showed that the two will 29 be equal only when the airport’s demand remains constant over time, that is, Q/s = 0. 30 This directly speaks of the importance of the time path of the traffic growth, as pointed 31 out by Oum and Zhang (1990): To maximize social welfare, airports should be allowed 32 to take losses or make profits at different times, seeking cost recovery only in the 33 long run. 34 What is perhaps more interesting in Zhang and Zhang (2001)’s finding is that under 35 the short-term cost recovery, airport charges are high when the demand is low and there 36 is excess capacity. However, when the demand is high, and there is congestion, airport 37 charges would be low. This seems to be undesirable. On the other hand, under the 38 long-term cost recovery, airport charges grow together with the demand. 39

41 42 2.3 Airport Concessions and Pricing Effects: Public 43 and Private Airports 44 45 Given the increasing pressure on public airports to self-finance their operations, airports 46 have been increasingly depending on revenues generated by non-aeronautical businesses,

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98 LEONARDO J. BASSO AND ANMING ZHANG

01 such as airport parking, in-airport stores and so on.4 The demand for these concession 02 services is complementary to the demand for aeronautical services, in that the more 03 people there are using the airport, the higher the concession revenues. Zhang and 04 Zhang (1997) wanted to analyze what would be the socially optimal balance between 05 aeronautical revenues and concession revenues given the cost recovery constraint, and 06 how the associated pricing practices would look like. For this, they modified the public 07 airport’s problem Equations (1)–(2) by incorporating the fact that concession demand is 08 complementary to aeronautical demand: 09 10 + − − + + − 11 max Qd PQ CQ rK Q Xpdp pX cX PKp p (8) 12 13 st PQ − CQ − rK + Q pX − cX = 0 14 15 In Equation (8), p represents the price for concession goods or non-aeronautical services 16 provided in the airport, Xp is the demand for concession services per flight, and cX 17 are the costs of providing the concession services, which are assumed to feature constant 18 returns to scale. 19 There are two important things to note in the above setup. First, the complementarity 20 between the demands is unidirectional, that is, consumers’ decision to fly or not is based 21 on the full price of the aeronautical service; they do not take into account the price 22 of the concessions in their travel decisions. Only after arrival at the airport, passengers 23 observe concession prices and make purchasing decisions. Second, note that the budget 24 constraint in Equation (8) includes the revenues from both aeronautical and concession 25 services, which effectively enables cross-subsidies between the two services. 26 Without the budget constraint, the (first best) optimal solution obviously involves 27 marginal cost pricing on the concessions side, i.e., p = c X. On the aeronautical side, 28 the social-marginal-cost pricing of Equation (3) would have an additional markdown; 29 this happens because, now, a smaller aeronautical charge increases the demand for both 30 aeronautical services and concessions services. Hence, the optimal aeronautical charge is 31 smaller. This would, however, lead to deficits if the delay function is non-homogenous of 32 degree one in the traffic to capacity ratio, as discussed above. With the budget constraint, 33 and assuming that the delay function is non-homogenous of degree one, Zhang and 34 Zhang showed that at the (second best) optimal solution of problem (8), the price of 35 concession services would be such that p>cX, showing that profits would be made 36 in concession services. Therefore, concession operations would subsidize aeronautical 37 operations. If the airport were not allowed to make profits from its concessions, but was 38

39 40 4 For the last two decades, concession revenues have grown faster than aeronautical revenues; as a result, 41 they have become the main income source for many airports. At medium to large US airports, for instance, 42 commercial business represents 75–80% of the total airport revenue (Doganis 1992). Furthermore, concession

43 revenues have grown faster than aeronautical revenues. For example, in 1979, Hong Kong International Airport generated similar amounts of revenue from its aeronautical and non-aeronautical (mostly concession) 44 operations. In the late 1980s and 1990s, however, its concession revenue accounted for 66–70% of total 45 revenue (Zhang and Zhang, 1997). More importantly, concession operations tend to be more profitable than 46 aeronautical operations (see e.g., Jones et al., 1991; Starkie, 2001).

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01 still asked to self-finance its operations, then this would obviously lead to a smaller level 02 of social welfare. Furthermore, Zhang and Zhang showed that the cross subsidy from 03 concessions does not in general restore social-marginal-cost pricing on the aeronautical 04 side – Equation (2) – unless the demands and costs fulfill a very particular condition. 05 The attention to concession revenues, however, does not stop at the pricing and cost- 06 recovery issues of public airports. It has also been suggested that the complementary 07 nature of the concessions demand would give incentives for private airports to reduce the 08 price they charge for aeronautical services in order to maximize the number of travelers 09 in the airport using the concessions. This may imply that ex ante price regulations may 10 be unnecessary (see, e.g., Condie, 2000; Starkie, 2001). In order to assess whether the

11 argument holds, Zhang and Zhang (2003) and Oum et al. (2004) used Zhang and Zhang

12 (1997)’s model to look at the decisions a private unregulated airport would make. The

13 profit-maximization problem faced by a private unregulated airport is

14 max PQ − CQ − rK + Q pX − cX (9) 15 PKp 16 Zhang and Zhang (2003) and Oum et al. (2004) found that, while airside private prices 17 diminish as it was conjectured by Condie (2000) and Starkie (2001), they decrease less 18 than the prices in a public airport that also has concessions, and that this is the case 19 for both the first-best pricing (unconstrained public airport) and second best-pricing 20 (budget-constrained public airport). Therefore, concession revenues would not be a 21 valid argument for de-regulation once an airport is privatized. The intuition of the 22 result is simple: a private airport would care about the extra profits it can make from 23 concession activities; a public airport maximizing social welfare, however, would care 24 about concession profits but also about the consumer surplus induced. Consequently, 25 the decrease in the aeronautical charge would be larger in the public case: concession 26 revenues would actually increase the gap between private and public airside charges. 27 As for the effects of privatization on capacity decisions, Oum et al. (2004) obtained 28 that the capacity investment rule of the private airport would be the same as the one a 29 public airport follows, as in Equation (4). Hence, they argued that, if the capacity can 30 be adjusted continuously, the capacity investment decision of the private unregulated 31 airport would be efficient from a social viewpoint. However, since the price and capacity 32 decisions are jointly determined, and the pricing rules of the two airport types are 33 different, so will be the actual levels of traffic and capacity. In fact, since a private 34 airport charges more, its actual capacity would be smaller. But, their main point is that, 35 conditional on traffic level Q, the capacity K determined by Equation (4) would be 36 efficient because marginal benefit equals marginal cost. In line with the actual capacity 37 of private airports being smaller when capacity can be adjusted continuously, Zhang 38 and Zhang (2003) found that, when capacity is indivisible, a private airport would make 39 the (lumpy) addition of capacity later than a public airport. Note that none of these two 40 results imply anything about the level of actual delays, because traffic levels will be 41 different as well. 42 Czerny (2006) also looked at the effects of concession revenues on airside charges. 43 There are two important differences between his and Oum et al.’s model (2004): First, he 44 considers an airport that is non-congestible and has spare capacity, making the reasons 45 for cross-subsidization discussed above vanish. Second, in Oum et al. (2004) the number 46 of actual flyers would depend only on the full price and not on the price for concession

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100 LEONARDO J. BASSO AND ANMING ZHANG

01 services. The price of concession services would only determine how many of those who 02 are already flying buy concession services. Czerny (2006), however, considered that both 03 airport and concession charges affect the number of flyers, and that the complementarity 04 arises because only people who are actually flying will be able to purchase concession 05 goods. Hence, in Czerny’s setting it may happen that the airport charge is higher than 06 a consumer’s willingness to pay for flying, but that negative payoff is compensated by 07 positive benefits arising from consumption of commercial services. These differences 08 are material. Czerny showed that in this setting, the monopoly charge for aeronautical 09 activities is actually higher with concession revenues than without concession revenues, 10 thus rejecting the conjecture of Condie (2000) and Starkie (2001). The intuition is as 11 follows: when the airport has concession services, and since these influence the number 12 of flyers, the airport may increase its revenues in two ways. It may increase the price 13 for aeronautical services, using a low concessions charge to mitigate the decrease in

14 demand, or it may decrease its aeronautical charge, hoping to make revenues on the

15 concessions side. But since only passengers can buy commercial services, the demand

16 for the latter is a subset of the demand for flights. Therefore, an increase in aeronautical

17 charges increases revenue more than an increase in the concession services charge.

18 19 2.4 Efficiency Implications of Alternative Forms of Regulation 20

21 Traditionally airports have been owned by governments (national or local). Privatization

22 of major airports started in the late 1980s, and airport privatization has now become 5 23 an important phenomenon around the world. Most of the privatized airports have been

24 regulated out of the market-power concern given the monopoly nature of airports. Oum

25 et al. (2004), Lu and Pagliari (2004) and Czerny (2006) analyze the effects of alternative

26 mechanisms of regulation on the performance of private airports, with a particular focus

27 on how revenues from concession services should be dealt with.

28 Oum et al. (2004) have considered four different regulation mechanisms: single-till

29 rate of return (ROR), dual-till ROR, single-till price cap and dual-till price cap. Under

30 the single-till ROR, airport charges (for both airside and concession operations) are set for cost recovery plus a fair return on the invested capital. If u is the allowed ROR, then 31 the new problem the private airport solves is 32 33 max PQ − CQ − rK + Q pX − cX 34 PKp (10) − + − = 35 st PQ CQ Q pX cX uK 36 The well-known problem with ROR is that, if the allowed return is greater than the cost 37 of capital, i.e., u>r, the airport has an incentive to over-invest in capital, a problem 38 known as the Averch–Johnson effect. However, if the regulators get the allowed return 39

40 41 5 In 1987, the British government privatized the BAA, which owned and operated the three London airports 42 (Heathrow, Gatwick, and Stansted), among other airports in the UK. Since then, many airports around the

43 world have been or are in the process of being privatized. The majority stakes of Copenhagen airport, Vienna airport, Rome’s Leonardo Da Vinci Airport and 49% of Schiphol airport have been sold to private sector 44 owners. Many other European airports are in the process of being privatized. Major airports in Australia 45 and New Zealand have been privatized as well. As a way to partially privatize airports, six Chinese airport 46 companies including seven airports have been listed on stock exchanges.

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01 right, the problem vanishes. It has been argued though that, even if the allowed return 02 is chosen correctly, the single-till ROR would still misplace the incentives on terms of 03 the productive efficiency, because it is essentially a cost-based mechanism. While the 04 argument is sensible and has been detected empirically in several industries, it does not 05 flow analytically from model (10). 06 Under the dual-till ROR, the allowed return applies only to aeronautical operations. 07 If the regulators get the allowed rate right, the new restriction is PQ − CQ = rK.In 08 this case, the airport would make no profits in airside operations and, therefore, would 09 try to maximize QpX − cX, the profits coming from concession operations. Given 10 the complementary nature of the concessions demand, the airport will, in fact, try to 11 maximize traffic, which is equivalent to minimize the full price . Hence, this regulation 12 mechanism would lead to a capacity rule as in the public case, that is Equation (4), and 13 to average cost pricing, that is P = CQ + rK/Q. Note, however, that if u>r, the 14 Averch–Johnson effect re-appears. 15 We now turn to the price-cap regulation, a mechanism in which the regulator sets ∗ 16 a ceiling for the aeronautical charge, that is P ≤ P . Theoretically, the cap is set to 17 limit the airport’s market power, while ensuring its financial viability (this may include 18 a fair rate of return on capital investment). The difference between the single-till and 19 dual-till price-cap regulations is, again, related to whether concession revenues will be 20 lumped together with airside revenues or not; to be perfectly clear, the debate is not 21 about regulating concession activities. Under the single-till price-cap regulation, the cap ∗ 22 P will be set considering that the airport will likely make profits from concession 23 activities. This would imply, according to Oum et al. (2004), a cross-subsidy, just as 24 in the case of a public airport subject to budget constraint (Zhang and Zhang, 1997). 25 However, a problem is that the more profit the airport makes from concessions, the 26 smaller the allowed aeronautical charge would be in future revisions of the cap, even 27 if traffic grows and congestion builds. Because of this, the single-till cap regulation 28 for the case of congested airports has been criticized (e.g., Starkie, 2001): the airport 29 charge would not be a useful signal to users regarding congestion. Moreover, Oum 30 et al. (2004) also showed that a price cap (either single-till or dual-till) induces under- 31 investment in capacity, worsening the problem. Here, the airport is unable to recoup 32 fully from its investment in capacity – which reduces congestion and hence increases the 33 users’ willingness to pay – because the price is capped. Under the price-cap regulation, 34 therefore, while the market-power distortion is alleviated, the service-quality provision is 35 sub-optimal, suggesting an interesting trade-off between with and without the regulation. 36 This result is in fact very robust. Spence (1975) showed that if a monopolist who initially 37 can choose both price and quality of its product is constrained to charge below some 38 price ceiling, the quality it chooses will be always below what is socially optimal for that 39 price. It is noted that under the dual-till price cap, that is, when concessions revenues 40 are not considered in establishing the cap, Oum et al. (2004) showed that the cap would 41 not be set as low as in the single-till, something that seems desirable. 42 Hence, overall, Oum et al. (2004) concluded that the presence of the concession rev- 43 enues make the dual-till ROR approach a quite interesting mechanism as it would induce 44 the airport to invest optimally in capacity, while minimizing its costs and congestions 45 delays, since it would try to minimize the full-price. Indeed, Spence (1975) suggested 46 that ROR has nice properties when regulating both quantity and quality.

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102 LEONARDO J. BASSO AND ANMING ZHANG

01 Like Oum et al., (2004) and Lu and Pagliari (2004) have looked at the effects of single- 02 till and dual-till price cap regulations. They used a social-welfare function as the one 03 maximized in Equation (1), but considered that more traffic caused no congestion, that 04 is D = 0. The difference is that in a model with a delay function being non-homogenous 05 of degree one, congestion is essentially a cost. And given that the cost increases more 06 pronouncedly as the traffic gets closer to capacity, equilibrium levels of traffic would − 07 never surpass capacity (e.g., when DQ K = QKK − Q 1, delays approach infinity 08 when output approaches capacity). In Lu and Pagliari’s case, however, if the aeronautical 09 charge is too low, demand may well exceed capacity, particularly because in their model, 10 capacity is assumed to be fixed. Lu and Pagliari found that a single-till price cap would 11 be appropriate when the average cost of the airport is greater than the market clearing 12 price (for the given capacity), because cross-subsidies from concession revenues would 13 be needed to reduce the airside charge and restore full capacity use. In other cases, 14 however, they found that a dual-till price cap would be better: under the single-till the 15 price cap may be set “too low,” owing to the cross subsidy from concessions, and hence 16 dead-weight losses would occur because of excess demand. 17 Czerny (2006) also compared the single-till and dual-till price-cap regulations. As 18 discussed previously, he examined an airport that is non-congestible and has spare 19 capacity, and considered that both airport and concession charges affect the number of 20 flyers. Under these conditions, he found that the single-till dominates the dual-till in 21 terms of social welfare, a result similar to what Lu and Pagliari found when the airport 22 does not suffer from excess demand. The intuition is that with the single-till price cap, 23 the regulator has better control of the overall profits of the airport, which is not the case 24 with the dual-till regulation. Thus, the single-till helps to limit market power. 25 Hence, overall, when the airports are not congested, a single-till price cap seems like 26 a reasonable approach to control market power. However if congestion actually occurs, 27 the single-till would induce incorrect signals regarding congestion, while the dual-till 28 would distort capacity investments. Furthermore, if there are delays as traffic levels 29 approach capacity (as in the original setup), the socially optimal pricing structure would 30 require cross-subsidization (Zhang and Zhang, 1997), but this is precluded in the dual- 31 till. Hence, in congested airports, the dual-till ROR regulation may be a better option: 32 the incentives for capacity investments would be well placed, while the regulated airport 33 would pursue average cost pricing. 34

35 36 2.5 Airport Pricing Considering Environmental Costs 37 Carlsson (2003) developed a model of airport pricing that, in addition to congestion, 38 also includes environmental damages (noise, emissions).6 For this, he modified the 39 social-welfare function in Equation (1) to include environmental costs, as follows: 40

42 6 43 Air travel is considered a rapidly growing source of greenhouse gases (GHGs), something that has sparked concern. The problem is that, while airport delays result in aircraft’s holding/circling in the air waiting for 44 landing and hence cost to airlines, the circling also burns extra fuel increasing GHG emissions. Furthermore, 45 the possibility of being held up induce airlines to carry extra fuel in their aircrafts, which increases the aircraft’s 46 weight and, consequently, its consumption of fuel and GHG emissions (see Economist, 2006).

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INTERPRETATIVE SURVEY OF ANALYTICAL MODELS 103

01 02 max Qd + PQ − CQ − rK − QE DQ K (11) P 03 04 05 where E is the average environmental cost per flight. It depends on the level of conges- 06 tion because, for example, the delay increases fuel consumption and hence emissions. 07 Carlsson considered many periods throughout the day and allowed the environmental 08 costs to vary according to the type of aircraft. For simplicity we do not do so here; the 09 intuition of the results remains unchanged. The optimal pricing obtained has two more 10 terms than the congestion-only social-marginal-cost pricing in Equation (3) when = 0. 11 He gets 12 13 D E D P = C + Q + E + Q (12) 14 Q D Q 15 16 The last two terms in the RHS of (12) represent the marginal environmental cost: 17 In addition to the airport’s marginal cost and the marginal cost of congestion, each 18 aircraft would have to pay the environmental cost it produces, plus another sum owing 19 to the fact that the extra delay a new flight imposes on existing flights, increases the 20 average environmental cost of all flights.7 These last two terms are obviously positive, 21 which shows that, when environmental costs are considered, the airside charge is higher. 22 Carlsson then pointed out that, if the proceeds from the environmental charge accrue to 23 the airport, then cost recovery may be feasible. Whether this is the case or not, however 24 is an empirical matter, as it depends heavily on the shapes of the delay function and the 25 average environmental cost. 26 As for the capacity decision, although Carlsson did not look into it, it is fairly evident 27 the direction in which it would change with the added environmental costs. Since now 28 more capacity is beneficial not only because smaller delays decrease the full price, but 29 also because smaller delays reduce average environmental costs, the socially efficient 30 capacity investment rule would induce a larger investment in capacity. 31

33 34 3 THE VERTICAL STRUCTURE APPROACH 35

36 TO AIRPORT PRICING

38 The vertical structure approach is newer and, hence, there are fewer papers. Here we

39 review Brueckner (2002), Pels and Verhoef (2004), Raffarin (2004), Basso (2005) and

40 Zhang and Zhang (2006). In this approach, the airline market is formally modeled as an

41 oligopoly, which takes airport charges and congestion taxes as given. Airports, however,

42 are not always considered integrally; in some cases, only airport authorities, who need to

44 45 7 The optimal charge is differentiated between types of aircraft and times of the day when these are 46 differentiated.

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104 LEONARDO J. BASSO AND ANMING ZHANG

01 set a tax to be paid in addition to the airport charge – implicitly assumed to be marginal 02 cost – are considered. In these cases, airport profits do not enter the social-welfare 03 function. 04 This airport–airlines approach to airport pricing was driven by the policy need to 05 respond to an increasing level of delays at hubs throughout the world. An important 06 characteristic of hub airports is that usually a few major airlines dominate the airports: 07 these are not atomistic carriers and hence they are not price takers. The focus of the 08 approach has mainly been on the characterization of optimal (public) runway pricing 09 under congestion and airline market power, as can be see from Table 2. Thus, the idea 10 has been to highlight the differences between the airport congestion pricing and the road 11 congestion pricing, where decision makers (individual drivers) are atomistic. Until most 12 recently, capacity was assumed to be fixed, and hence was not a decision variable of the 13 airport or the airport authority, in the vertical structure approach. 14 Brueckner (2002) should undoubtedly be credited for starting this stream of literature. 15 In this very influential paper, he considers N airlines that are seen as homogenous by 16 consumers and that compete in a Cournot fashion. He allows for peak and off-peak 17 demands, which are interrelated, and where the peak period consists of a set of relatively 18 short time intervals containing the daily most desirable travel times. Only the peak is 19 congested. From this setup, it would seem that the peak and off-peak travel are vertically 20 differentiated in that, other considerations such as income and congestion levels being 21 absent, consumers would prefer traveling in the peak period to traveling in the off-peak 22 period. In fact, Brueckner does not directly assume downward sloping demands, but 23 starts with a continuum of consumers who would decide to use the peak or the off-peak 24 periods (or not traveling by air at all) depending on the full prices they face: airfare, 25 plus congestion costs caused by delays at the airports. However, Brueckner also adds 26 a “tendency to fly in business,” which correlates to travel in the peak, as a device that 27 would enable simpler (non-corner) solutions. The problem with this is that it actually 28 imposes that in terms of pure utility, with no income or congestion effect whatsoever, 29 some consumers would prefer traveling in the off-peak period. This seems to contradict 30 the idea of the peak period being “the most desirable travel times.” 31 The airlines, observing the demands and understanding how consumers’ decisions 32 are made, choose their quantities in the output market. An important aspect here is 33 that congestion also affects airlines: There are externalities in production in that, the 34 more a rival produces, the higher a firm’s marginal and average costs will be. The 35 delay function is not necessarily linear in traffic. In equilibrium then, the sorting of 36 consumers towards peak and off-peak occurs through the airlines’ quantity decisions 37 (for given airport charge and capacity). Brueckner then looks at what should be the 38 optimal additional tax that should be charged to airlines in the peak period, in order to 39 adequately account for the congestion externality. Since the off-peak period is assumed 40 to be non-congested, no congestion toll would be needed. Thus, he looks at the regulator 41 case in the sense that the airport is not formally incorporated into the analysis: its profits 42 do not enter the social-welfare function, which is composed of only consumer surplus 43 and airlines’ profits, and there is no consideration of cost recovery, something that has 44 drawn important attention within the traditional approach (see Section 2). Brueckner’s 45 main conclusion – the one that has since driven research in the area – is that with 46 Cournot oligopoly, each airline will internalize the congestion imposed on its flights

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01 ) 02

04 Continued ( 05

12 frequencies, prices. demand. They are onlysocial an cost. external 13 (peak-load pricing). airlines decisions. traffic and affects bothpassengers airlines and affects both airlines and passengers One period (congestion pricing). Three stage game: airport pricing, Congestion does not affect airlines nor Delay is a linear function of traffic Observations There are peak and off-peak periods Sorting to periods is endogenous through Only the peak isCongestion congested is a non-linear function of One period (congestion pricing). Delay is a linear function of traffic and 14

16 − 17 + regulator 18 + + + 19 CS CS CS 20 = = = 21

22 congestion costs. airport, only a modeled, only two regulators. 23 Single airport. airport modeling Max SW No formal modeling of the Two airports not formally Max SW Also analyze Individual Max SW Max SW 24

30 airlines in

31 N homogenous Cournot Duopoly in homogenous Cournot Differentiated duopoly competing in prices and frequencies

33 Vertical Structure Approach 34

40 Optimal tax (additional to airport charges) to account for congestion Optimal tax (additional to airport charges) to account for congestion and market power Efficient congestion pricing

42 Summary of Papers Using the 43

46 Table 2 AuthorBrueckner (2002) Goal of the Paper Oligopoly modelPels and ObjectiveVerhoef Function and (2004) Raffarin (2004)

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13 traffic and affects bothpassengers. airlines and delay cost traffic affecting only the passengers.

14 Observations One period (congestion pricing). Congestion is a non-linear function of Consumers are also affected by schedule One period (congestion pricing). Congestion is a non-linear function of The demand function is general

16 17 + +

19 + +

20 CS CS = = 21

22 profits profits 23 airport modeling Max airports’ profits Max airport–airlines joint Max SW st BC Max individual airport Max airports’ profits Max SW st BC Two airports (round trips) Max SW Max SW

24 : airport profits; BC: Budget constraint.

25 —Cont’d

30 airlines in airlines in

31 N differentiated Cournot N homogenous Cournot

33 Vertical Structure Approach : airlines’ profits (industry wide);

36 airlines and 37 N 38

40 Optimal pricing to account for congestion and market power when there are prices and capacity capacity is variable 41

43 Summary of Papers Using the

45 Zhang and Zhang (2006) 46 Table 2 AuthorBasso (2005) Goal of the Paper Effects of ownership on Oligopoly model Objective Function and SW: social welfare; CS: consumer surplus;

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INTERPRETATIVE SURVEY OF ANALYTICAL MODELS 107

01 (and passengers) while ignoring the congestion externality imposed on other airlines’ 02 flights, which enables a limited role for congestion pricing by the airport authority.8 In 03 a “symmetric airlines” case, the optimal toll that should be charged during congested 04 periods is equal to the congestion cost from an extra flight times one minus a carrier’s 05 share. In particular, a monopoly airline would perfectly internalize all the congestion 06 it produces and hence there would be no room for congestion pricing. This shows the 07 difference with the road case: with market power, the degree of internalized congestion 08 is usually sizeable. 09 Pels and Verhoef (2004) attempted to expand Brueckner’s work in two directions: 10 first, they explicitly considered the market power distortion and its effect on the optimal 11 congestion toll. Second, they addressed the issue that, at an origin–destination (OD) 12 pair, the airports may not collaborate to maximize overall social welfare; instead, each 13 airport may maximize a local measure of welfare. Their model is as follows. Consider 14 an OD pair in which the airports decide charges prior to airline competition. The 15 capacities of the airports are assumed to be fixed. In this OD pair, two homogenous 16 and symmetric airlines compete in Cournot fashion, taking airport charges and taxes as 17 given when they choose their quantities (frequencies). Congestion delays affect airlines 18 costs; the delay function is a linear function of total traffic at an airport. Passengers 19 choose airlines based on a generalized cost which is the sum of the air ticket and 20 congestion delay costs, and their demand for air travel is roundtrip-based. The model 21 is solved by backward induction to obtain sub-game perfect equilibrium. Hence, the 22 first step is to solve the airlines’ oligopoly, in order to obtain a sub-game equilibrium 23 which will be parametrically dependent on the congestion tolls charged at each airport. 24 With that sub-game equilibrium at hand, the authors looked for the optimal taxes that 25 should be charged at each airport in order to adequately account for congestion. Initially, 26 they consider that a single authority handles both airports and, consequently, maximizes 27 the sum of consumer surplus and airlines’ profits. Hence, like Brueckner (2002), Pels 28 and Verhoef looked at the regulator case, in that the airports’ profits do not enter the 29 social-welfare function. 30 Their main result indicates that the optimal toll would have two components: a 31 congestion effect (which is positive) and a market power effect (which is negative). 32 The first part is the one identified by Brueckner: since airlines only internalize the 33 congestion they imposed on themselves, the uninternalized congestion should be charged. 34 The second term, which decreases the toll, arises because of the market power at the 35 airline level. What happens is that the regulator, in maximizing social welfare, would 36 need to subsidize the airlines to induce them to produce more. The sign of the optimal 37 toll is therefore undetermined; in particular, when the market-power effect exceeds the 38 congestion effect, a subsidy would be the result. The toll would be positive if the 39 congestion effect dominates. They pointed out, for example, that this would undoubtedly 40 be the case for a monopoly airline. 41

43 8 As indicated above, Brueckner obtained the result by developing a model that explicitly recognizes the 44 congestion’s effect on airfares. It is noted that Daniel (1995) first raised the internalization issue and developed 45 a detailed simulation model to analyze carriers’ self-internalization and calculate congestion tolls that exclude 46 the internalized congestion.

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108 LEONARDO J. BASSO AND ANMING ZHANG

01 Pels and Verhoef compared their toll to the pure congestion toll suggested by 02 Brueckner (2002). They found that, when the market-power effect is strong, a pure 03 congestion toll may actually be harmful for social welfare, since airlines are charged 04 with a tax when in fact they should be receiving a subsidy. Brueckner did acknowledge 05 this, though, by stating in his proposition that, “since congestion pricing corrects one 06 distortion but leaves the residual market-power effect in place, tolls are guaranteed to be 07 welfare improving only if that effect is sufficiently small. Otherwise, a negative welfare 08 effect is possible” (p. 1367). Pels and Verhoef argued that, if a negative toll (subsidy) 09 is optimal but unfeasible (for example for political reasons) the regulator should charge 10 a zero toll. 11 As indicated above, Pels and Verhoef also considered the case in which, at each 12 airport, different regulators only maximize consumer surplus of passengers that live in 13 the airport’s region, plus the profits of the home airline. The non-cooperative behavior of 14 airports obviously implies that the result will be inferior to the single-regulator case. In 15 fact, the authors showed, both numerically and analytically, that in the non-cooperation 16 case, tolls at each of the two airports would always be positive. 17 Raffarin (2004), like Brueckner (2002) and Pels and Verhoef (2004), was interested 18 in the optimal airport toll. But rather than considering a two-stage model, she considered 19 a three-stage model. In the first stage, the airport chooses its price. But then, conditional 20 on the airport charge, duopoly airlines sequentially decide frequencies and then prices. 21 The difference with Brueckner and Pels and Verhoef is that, in their case, airlines only 22 decided frequencies; the price is determined in equilibrium by the Cournot assumption. 23 Raffarin, however, has a system of differentiated demands (obtained from a representa- 24 tive consumer framework) such that an airline’s demand increases when its frequency 25 increases or price decreases, and decreases when its rival’s frequency increases or price 26 decreases. 27 Raffarin’s model has three key assumptions that determine her results: first, she 28 assumes that, even though frequencies are airlines’ decisions, any demand will always 29

30 be fulfilled. And this is not ensured by the airlines’ choice of aircraft size, k, because k

31 is an exogenous parameter in the model (i.e., equilibrium results will be dependent on

32 k). Hence, there is no real connection between the number of passengers and the number

33 of flights, other than the assumption that there will be enough space. Both Brueckner

34 (2002) and Pels and Verhoef (2004) made a “fixed proportions” assumption, by which

35 the number of passengers in a flight is a fixed constant. This assumption makes it easier,

36 yet transparent, to transform the demand in terms of passengers, into an airport’s demand

37 in terms of flights. The second assumption is that congestion delays – which as in Pels

38 and Verhoef (2004) increase linearly with total traffic – do not affect consumers’ or

39 airlines’ decisions. Instead, congestion costs are subtracted in the social-welfare function,

40 which, interestingly, explicitly includes the airport’s profits. Hence, in this case, airlines 41 do not internalize any of the congestion they cause because it does not directly affect 42 them (it is not a cost to them), and passengers do not care about congestion either. 43 Finally, the third important assumption is that an airline’s operational cost per flight, z, 44 depends on the aircraft size in an increasing fashion, that is dzk/dk>0. Hence, even 45 though using larger aircraft means fewer flights, which saves on costs, each of those 46 flights will be individually more costly. Aircraft size, however, is not a decision variable

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INTERPRETATIVE SURVEY OF ANALYTICAL MODELS 109

01 but a parameter. Hence, the implication is that, for given airport charges, equilibrium 02 frequencies increase as the aircraft size diminishes. 03 Rafffarin then maximizes social welfare – which is the sum of the airport’s profits, 04 airlines’ profits and consumer surplus, minus congestion costs – in order to find what 05 the optimal frequencies are, that is, the optimal level of airport’s demand. The optimal 06 airport charge is then obtained as the price that would induce the optimal frequencies. 07 The optimal charge she obtained has three components (which she did not recognize): the 08 airport’s marginal cost, plus the cost of congestion (recall that airlines do not internalize 09 any fraction of congestion in this model), plus a third term. This third term is negative, 10 and could be assimilated to Pels and Verhoef’s market-power effect. The interesting 11 twist, however, is that this term depends on the aircraft size, k, and diminishes the higher 12 k. That is, the airport charge should be larger for smaller aircraft. And since aircraft size 13 and weight are positively correlated, this implies that the airport charge should decrease 14 with the aircraft weight, rather than increase as it is usually the case. The airport would 15 reward airlines that use larger aircrafts because that implies smaller frequencies and 16 hence smaller congestion costs. The choice of k, however, is not endogenous for the 17 airlines in the model. 18 The three papers we have reviewed so far have in common two important features: 19 they all consider maximization of social welfare and in all the three cases, the airport 20 capacities are fixed. In closely related but independent work, Basso (2005) and Zhang 21 and Zhang (2006) generalized these two aspects. Both papers considered that the airport 22 decides on price and capacity in the first stage, and in the second stage N airlines 23 choose quantities (frequencies) in the output market. The airlines have identical cost 24 functions; they are insensitive to congestion costs in Zhang and Zhang (2006) while 25 they do bear extra costs owing to congestion in Basso (2005). Passengers, as usual, 26 are sensitive to the full price of travel, that is, the airline ticket plus congestion delay 27 costs.9 Both used congestion delay functions that are not homogenous of degree one in 28 the traffic to capacity ratio, that is, congestion increases more than linearly with total 29 traffic (for a given level of capacity). Other differences between the two papers are 30 Zhang and Zhang considered that airlines are homogenous in the eyes of the consumers, 31 while Basso allowed them to be horizontally differentiated (in a “non-address” fashion). 32 Basso also considered in the full price perceived by the passengers another time cost, 33 namely, schedule delay cost. This time cost arises because flights do not depart at a 34 consumer’s will but have a schedule. Hence, schedule delay costs are a sort of waiting 35 time, which decreases with higher airline frequencies. On the other hand, Zhang and 36 Zhang considered a general demand function (of the full price) while Basso considered 37 a more restrictive system of demands: linear in the full-prices of airlines. 38 Both Basso (2005) and Zhang and Zhang (2006) solved the airport–airlines game 39 by backward induction, characterizing the shape of the derived demand for the air- 40 port through comparative statics. Then, they both considered three different objective 41 functions (Basso considered two more which are discussed later): unregulated profit 42

44 9 This last point is enough for the internalization of own congestion by an airline to arise in oligopoly, as 45 discussed earlier. It is not needed for both, airlines and consumers, to be sensitive to congestion costs in order 46 to derive the result.

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110 LEONARDO J. BASSO AND ANMING ZHANG

01 maximization, unconstrained social-welfare maximization, and social-welfare maximiza- 02 tion subject to cost recovery. Let us first discuss the pricing rules they obtained. In the 03 case of unconstrained maximization of social welfare, they both considered a welfare 04 function in which the airport’s profit is included. They found that, in their more general 05 settings, Pels and Verhoef’s insight goes through: the optimal pricing rule is the sum 06 of airport’s marginal cost, plus a congestion effect (positive) and a market-power effect 07 (negative). When capacity is fixed, this pricing rule shows that with large values of N, 08 the congestion effect is large while the market-power effect is weakened. Smaller values 09 of N, on the other hand, imply a weaker congestion effect but a stronger market-power 10 effect. With this pricing rule, the airport manages to obtain a “first best” outcome (subject 11 to the market structure of the airline market which may be of monopoly or oligopoly) 12 in the airline market. Note that, in this setting, rather than a regulator setting the toll, it 13 is the airport that would distort marginal cost pricing to account for both uninternalized 14 congestion and market power. Since the optimal airport charge may be below marginal 15 cost and even below zero, the airport may run a deficit. 16 In the case of unregulated profit maximization, Basso (2005) and Zhang and Zhang 17 (2006) clearly found, in the pricing rule of the airport, the “double marginalization” 18 problem that affects an uncoordinated vertical structure of airport and airlines. For a 19 given capacity, the airport charge will decrease with the number of airlines downstream. 20 On the other hand, and in a somewhat expectable result, an airport that maximizes social 21 welfare subject to cost recovery will have a charge that is in between the unconstrained 22 welfare-maximizing charge and the profit-maximizing charge. The balance will be given 23 by the severity of the budget constraint. 24 Turning to capacity decisions, Basso (2005) and Zhang and Zhang (2006) found that an 25 unconstrained welfare-maximizing airport will provide capacity until the marginal cost 26 of capacity equates the marginal benefits in reducing delays (to airlines and passengers 27 in the case of Basso, to passengers only in the case of Zhang and Zhang). Interestingly, 28 Zhang and Zhang (2006) proved that when both price and capacity are decision variables, 29 in their setting, the market structure (i.e., N) has no impact on airport’s actual demand 30 and capacity. Consequently, delay levels will be independent of market structure. This 31 however does not hold in Basso’s setting, in which airlines are differentiated and/or 32 passengers care about schedule delay cost. The explanation has to do with the “preferred 33 N” of a welfare-maximizing airport. Basso showed that there are two opposing effects. 34 With the congestion and market power effects being controlled, as it is the case here, 35 fewer airlines in oligopoly would provide – each of them – higher frequencies than more 36 airlines, thus delivering smaller schedule delay costs which increases social welfare. 37 Smaller N would be preferable. On the other hand, differentiation brings about new 38 demand when N increases, so a larger N is preferable. 39 An unregulated private airport, however, would increase its capacity until the marginal 40 revenue of doing so equates its marginal cost. Clearly, this capacity rule is different from 41 the previous one. Basso (2005) noted then, that this is different than what happened 42 in the traditional approach (e.g., Oum et al., 2004), in which the capacity rules of 43 unregulated private airports and unconstrained public airports were the same. However, 44 when N goes to infinity, i.e., airlines become perfectly competitive, the capacity rules 45 become the same. The explanation for this is given in the next section. Further, Zhang 46 and Zhang, and Basso, showed that conditional on the level of traffic, a private airport

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01 would over-supply capacity. However, that capacity would most likely be too small in 02 a second-best sense. That is, a public airport that is forced to charge using the private 03 airport pricing rule, would most likely supply more capacity than the actual capacity 04 offered by the private airport (Basso, 2005). As with price, a budget constrained airport 05 would, conditional on the level of traffic, choose a level of capacity that is in between 06 the private capacity and the unconstrained public capacity. 07 Basso looked at two other types of ownership as well. First, he investigated the 08 case in which airports and airlines vertically integrate. The reason to look at this is 09 because it has often been argued that more strategic collaboration between airlines and 10 airports would solve incentive problems, particularly regarding capacity expansions. 11 Basso found that the airport charge would include marginal cost and a term equal to the 12 uninternalized congestion cost of each carrier, but would also include a third term, which 13 is positive. This mark-up is put in place to fight against the business-stealing effect, 14 a horizontal externality typical of oligopoly: a firm does not take into account profits 15 lost by competitors when expanding its output. By increasing the airlines’ marginal cost 16 with a higher airport charge, the airport would be able to induce a profitable (for the 17 combined vertical structure) contraction of total output. In fact, the final outcome is 18 indeed that of cooperation between competitors in the airline market. The intuition is that 19 airlines would “capture” an input provider to run the cartel for them, given that they are 20 unable to collude on their own. As for capacity, the vertically integrated structure would 21 have the same capacity rule as the unconstrained public airport. The actual capacity 22 however would be below the second-best capacity (i.e., a public airport that is forced 23 to charge using the vertical integration pricing rule would supply more capacity). Basso 24 also showed that, depending on how differentiated airlines are, and how strong schedule 25 delay effects are, profits may be higher when the airports integrate with a single airline. 10 26 A non-integrated private airport though will always prefer a larger N. 27 Basso (2005) also looked at the case in which two distant airports are privatized 28 separately. Social-welfare wise, the results worsen because the airports’ demands are 29 perfect complements: in his setup with only two airports, a trip that starts at one airport 30 necessarily ends at the other. Therefore “competition” between the airports induces a 31 horizontal double-marginalization problem. This horizontal double marginalization arises 32 in both the unintegrated and integrated vertical structures. 33

34 35 4 RELATIONSHIP BETWEEN APPROACHES 36 37 It is clear that the questions examined in the two approaches – which we have called 38 the traditional approach and the vertical structure approach – have not perfectly over- 39 lapped, and the two approaches appear rather different. This raises questions about the 40 transferability of results, something that seems quite important to clarify if one is to 41 apply to policy making, what has been learned from analytical models of airport pricing. 42

44 10 Both Brueckner (2002) and Zhang and Zhang (2006) had N airlines downstream. However, public airports 45 and vertically integrated airports would have no particular preference for N in their settings, because airlines 46 are homogenous and there are no schedule delay effects.

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112 LEONARDO J. BASSO AND ANMING ZHANG

01 We address the issue of the connection between the two approaches in this section, 02 based on results and discussions in Basso (2005). 03 In the traditional approach, the airline market is not formally modeled, under the 04 assumption that the airport charge would be completely passed to consumers, and that 05 airline tickets and other charges would be exogenous to the airport. Oum et al. (2004) 06 argue that this would be the case under perfect competition. In the vertical structure 07 approach, on the other hand, it is recognized that airports provide an essential service that 08 is required by airlines to move passengers; therefore, airports are viewed as providing 09 a necessary input for the production of an output: travel. In fact, some authors using 10 the vertical structure approach have been somewhat critical of the traditional approach 11 on the grounds that it does not properly consider all the actors involved. For example, 12 Raffarin (2004) said that it is rather strange that the pricing rules obtained from the 13 traditional approach do not consider passengers’ utility. However, this is not completely 14 accurate. Passengers are indeed somehow considered in the approach, as delay costs 11 15 affect them as well, something that Raffarin missed. On the other hand, a view of the 16 problem that recognizes that (i) airlines may have market power and (ii) airports provide 17 an input for the production of an output sold at another market, appears more complete. 18 Using the notations of Section 2, what the papers in the vertical structure approach 19 have shown is that for any given airport charge, P, and airport capacity, K, the airline 20 market – the downstream market – will reach some equilibrium. This equilibrium is 21 constituted not only by equilibrium traffic but also by equilibrium delays and air ticket 22 prices. By stressing this fact, three things become apparent. First, as far as the airport 23 is concerned, its demand will be some direct function of P K and of the (exogenous) 24 airline market structure, which in most papers is represented by the number of airlines 25 N. Hence, the airport’s derived demand would be QP K N. Delays enter the picture 26 through the equilibrium of the downstream market. How this demand faced by the airport 27 responds to changes in P and K is something that a formal analysis of the airline market

28 can unveil. Second, how airport charges and airlines’ delay costs are passed to consumers

29 is built inside the demand faced by the airport and hence depends in general on the

30 nature of the equilibrium reached in the airline market. In this sense, it would seem

31 that a full price model pertains more to the airline-market stage than the airport-market

32 stage. And third, other airline charges may not be exogenous to the airport because the

33 downstream equilibrium – that is, the airport demand – depends on P and K, which are

34 decided by the airport. Airport managers with foresight will take this into account and

35 decide user charges and capacity investment accordingly.

36 Thus, we can go back to the traditional approach and contrast its basic setting with

37 what we have described above. Two important questions arise: 38 1. Is it reasonable to use the full-price idea at the airport level, rather than at the airline- 39 market level? That is, under what conditions would it be legitimate to assume that 40 the airport demand can be written as Q – with = P + DQ K – rather than as 41 QP K N? 42

44 11 The problem might lie in that Morrison (1987) states that the final consumers of airports services are 45 airlines, even though in his model congestion explicitly affects passengers. In Oum et al. (2004), passengers 46 are said to be the final consumers.

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01 2. If under some conditions the airport demand can reasonably be written as Q, 02 would its integration give a correct measure of consumer surplus? We have learned 03 that the consumers of airports are both airlines and passengers. Hence, a social- 04 welfare function should include both airlines’ profits and passenger surplus. This 05 is in fact what is explicitly done in the vertical structure approach when analyzing 06 the maximization of social welfare. In the traditional approach, however, consumer 07 surplus has been obtained through integration of the airport demand function with 08 respect to a full price. Under what conditions does the derived demand for the airport 09 carry enough information about the downstream market so that its integration gives 10 a correct measure of airlines’ profits and passenger surplus? 11 In short, these two questions attempt to clarify how the two approaches are related to 12 each other. Basso (2005) analyzed this by using a vertical structure model to derive 13 the demand for the airport. Details of his modeling were presented in Section 3 but, in 14 short, he considered an airline oligopoly featuring N symmetric airlines, facing (linear) 15 differentiated demands, which are dependent on the vector of full prices. These full 16 prices are the sum of the airfare plus congestion delay costs. The important thing to 17 note here is that, as opposed to the traditional approach case, the full-price is used at the 18 airline market level rather than at the airport market level. 19 Solving the airline subgame, Basso found an equation which implicitly defined the 20 airport’s derived demand function QP K N. Examination of the equation allowed 21 Basso to show that, in general, Q would depend not only on = P + DQ K but 22 ≡ ≡ also on DQ D/Q and N. That is, in general, Q Q DQN. However, in the 23 “perfect competition” case, i.e. when N → under the Cournot conjecture, it is 24 → ≡ true that Q DQN Q. Thus, the answer to the first question above is: 25 Under perfect competition, a full price as defined by can in fact be used directly 26 at the airport-market level. It does summarize well the equilibrium of the downstream 27 market. 28 Now we turn to the second question: If we assume that there is perfect competition, 29 would the integration of Q correspond to the sum of airlines’ profits and passenger 30 surplus? This question is relevant because, if it is not the case, then even under perfect 31 competition the traditional approach would be maximizing a function that is not total 32 social welfare. This second question is related to the more general subject of the relation 33 between input and output market surplus measures (Jacobsen, 1979; Quirmbach, 1984; 34 Basso, 2006). Results from that literature, however, do not apply directly to this case 35 because, in the traditional approach, the integration of the airport’s demand is with 36 respect to the full price , rather than the airport charge P. To answer the question, Basso 37 (2005) computed, in subgame equilibrium, the surpluses of airlines and passengers. He 38 then showed that, when N →, and therefore one can reasonably write the airport 39 demand as Q, the integration of the airport demand with respect to would give 40 41 42 Qd = + PS (13) 43 44 45 where is the aggregate airlines’ profits, and PS is passenger surplus. Therefore, the 46 answer to the second question would be this: When there is perfect competition, such

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114 LEONARDO J. BASSO AND ANMING ZHANG

01 that using Q is justified, the integration of the airport demand with respect to the 02 full price will deliver a correct measure of consumer surplus, i.e., airlines’ profits plus 03 passenger surplus. 04 Perfect competition in the airline market was in fact the maintained assumption of 05 Oum et al. (2004). Hence, Basso (2005) provided a theoretical support for their claim. 06 But he also provided boundaries for the use of the traditional approach: it would be 12 07 reasonable to use it only if market power at the airline level is absent. If airlines 08 have market power, modeling the demand for the airport as Q would be incorrect. 09 Furthermore, Basso (2005) showed that its integration with respect to would actually 10 fall short of giving the sum of airlines’ profits and passenger surplus. In this case, a full 11 model that formally considers the airline market, as in the vertical structure approach, 12 would be necessary. 13 Lastly, since Q cannot be used when there is market power downstream, one may 14 wonder whether by using the demand function QP K N – which may be estimated 15 empirically for instance – and by integrating it with respect to P, one can adequately 16 capture airlines’ profits plus passenger surplus. This is not the case, unfortunately. Using 17 results in Basso (2006) it can be shown that the integration of the airport demand with 18 respect to P would give: 19 20 N − 1 N − 1 Q QP K NdP = + PS − Q D dP (14) 21 N N P Q 22 P P 23 Thus, there is no value of N for which the integral of the airport demand with respect 24 to P would be equal to airlines’ profits plus passenger surplus (not even if N is very 25 large). 26

29 5 PRICING OF AIRPORT NETWORKS

30 The papers we have reviewed, in both the traditional and vertical structure approaches, 31 do not really deal with airport networks. In most cases they deal with an airport in 32 isolation. The exceptions, so far, have been Pels and Verhoef (2004) and Basso (2005) 33 who consider a “network” of two airports. Yet, real air networks are obviously more 34 complex than that, and it is fairly clear that in these real airport networks other issues 35 arise. We review here three papers – namely, Oum et al. (1996), Brueckner (2005), and 36 Pels et al. (1997) – that have dealt with a network of airports, that is, three or more 37 airports. 38 Oum et al. (1996) argue that in hub and spoke (HS) networks, airports’ demands are 39 complementary because any take-off at a spoke airport will generate a landing at the 40 hub. This complementarity is of different nature than the complementarity that arises in 41

43 12 An important qualification here is that these results hold for the specific set-up that Basso (2005) used which, 44 for example, featured linear demands, Cournot competition and symmetric airlines with constant operational 45 marginal costs. An open research question is how these findings change under more general demand and/or 46 cost specifications, and other types of airline competition.

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01 two-airports networks because the presence of a hub introduces asymmetries. As in the 02 two-airport cases, failure to consider the complementarities when looking for optimal 03 pricing policies will result in social welfare losses. But in a HS network, congestion at 04 the hub will build up more rapidly than at spoke airports. And when budget adequacy is 05 an issue, this may imply the need for cross subsidizations between airports. Depending 06 on the type of ownership however, cross subsidies may be unfeasible. Oum et al. study 07 how ownership and cost recovery constraints affect airport pricing in a HS network and, 08 consequently, social welfare. 09 More specifically, Oum et al. (1996) consider n airports in a HS system: n-1 airports 10 are spoke airports and there is one hub. All the airports have constant operational 11 marginal costs and fixed capacity, but their capacity maintenance costs are positive. 12 The demands for these airports depend on the charges at both the hub and spoke 13 airports. All the airports are congestible, but congestion is an external cost that the 14 airport authority will include in the social-welfare function; it does not affect the 15 demands (as in Raffarin, 2004; see Section 3). This setup shows two things: First, 16 the spoke airports’ demands are indeed complementary with the hub’s demand, but 17 the demands are not directly complementary among the spoke airports. Second, that 18 this paper is ascribable to the traditional approach, since the airline market is not for- 19 mally included. Indeed, consumer surplus is measured as the integrals of the airports’ 20 demand. 21 Oum et al. first analyze the case in which all the airports are publicly owned and 22 under the control of a single authority: this is the “federal” case. The authority will 23 maximize the airports’ profits plus consumer surplus – the sum of the integrals of 24 airports’ demands – minus external congestion costs. The optimal pricing policy would 25 have all the airports charging SMC, that is, the operational marginal cost plus the external 26 costs of congestion. Since the hub is more likely to be heavily utilized, congestion will 27 be greater there than at the spoke airports. Hence, they assume that SMC pricing would 28 lead to cost recovery at the hub but to deficits at the spoke airports. The first-best federal 29 case then would require cross subsidies from the hub to the less utilized spoke airports. If 30 a budget constraint is set in place, the question becomes whether the hub makes enough 31 profits to cover for the spoke airports’ deficits. If it does, we are back in the first-best 32 case. If it does not, then Ramsey pricing is called for: the charge at the hub will increase. 33 Cross subsidization will be, obviously, still needed and this alternative will be welfare 34 inferior to SMC pricing. 35 They then look at the case in which each airport is under the control of a different 36 authority who, subject to cost recovery, maximizes its local social welfare, that is, 37 the integral of own demand plus own profits, minus congestion costs. This is the 38 “de-federalized” or “local government” case. Given the assumption about SMC not 39 covering costs in spoke airports, in this case, the hub will price at SMC, but the 40 spoke airports would charge average costs to ensure cost recovery. Since individual cost 41 recovery implies overall cost recovery, this case will be inferior, social-welfare wise, to 42 the previous Ramsey pricing case. In general, in the federal case, and independent of 43 whether SMC or Ramsey prices are used, charges at the hub will be larger and charges 44 at the spoke airports will be smaller than in the local government case. Oum et al. 45 (1996) conclude that de-federalization of airports may imply social welfare losses: by 46 not jointly pricing the airports, the local airport authorities will not take into account

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116 LEONARDO J. BASSO AND ANMING ZHANG

01 that demands are complementary and cross-subsidies will likely become unfeasible. The 02 welfare losses, though, would have to be balanced against possible X-inefficiencies gains 03 that de-federalization may bring about. 04 Recall, however, that the conclusion of Section 4 was that a traditional approach 05 would be justified only when air carriers are atomistic. What would happen if carriers 06 have market power? In this case, we would need a vertical structure type of approach. 07 This is what Brueckner (2005) analyzes. The main point here has to do with the meaning 08 of market power. One of the conclusions in Section 3 was that congestion tolls would 09 decrease in an airline’s share of flights at the airport, because an airline only internalizes 10 the congestion caused on own flights. Since in that section, only one or two airports 11 were considered, the share of flights at the airport was identical to the share of flights 12 at the city-pair market level. However, when one considers even a simple network 13 of airports in which airline competition exists, it is no longer true that the share of 14 flights at the airports will necessarily be equal to the share of flights at the city-pair 15 market level. Hence, the relevant question becomes – what is the relevant flight share 16 for congestion internalization? Brueckner considers the following network in which two 17 airlines compete. 18 19 5.1 Network Structure and Airline Competition (Brueckner, 2005) 20

21 In this network, airport H is airline 1’s hub, while airport K is airlines 2’s hub. Airline

22 1 serves four city-pair markets (depicted by the solid lines in Figure 1): AH, KH, BH,

23 and AB (two legs). Airline 2 also serves four city-pair markets (dashed lines). The

24 airlines compete in two markets, KH and AB, while each is a monopolist in its two other

25 markets. It can be easily recognized – for example under full symmetry – that airline 1’s

26 share of departures and take-offs at its hub H is larger than airline 2’s share. Similarly,

27 airline 2 dominates hub K in terms of departures and take-offs. However, in the two

28 markets where the airlines compete, they would both have a 50% share of flights under

29 symmetry. This nicely shows the difference between the shares of flights at airports and

30 the share of flights in city-pair markets, which justify the research question.

32 33 H 34

36 AB 37

40 K 41

42 43 Airline 1 44 Airline 2 45

46 Figure 1 Network Structure and Airline Competition (Brueckner, 2005).

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01 To analyze what would be the optimal congestion toll, Brueckner uses a setup 02 which essentially is the same as in his single-airport paper (Brueckner 2002; see 03 Section 3 for a description) but considers each of the various markets. Airports are 04 assumed to have a fixed exogenous capacity with only the hubs being prone to con- 05 gestion. The derivation of optimal congestion tolls is quite involved so it is omitted 06 here, but the conclusion is simple and important: Regardless of the degree of market 07 power that an airline has in the city-pair markets it serves, the amount of conges- 08 tion it internalizes depends only on its flight share at the congested airport. Hence, 09 “the appropriate airport congestion tolls are carrier-specific and equal to the conges- 10 tion damage from an extra flight times one minus the carrier’s airport flight share” 11 (Brueckner, 2005, Proposition 1, p. 612). 12 An important final point that Brueckner (2005) raised has to do with the market- 13 power effect we discussed in Section 3. There, we saw that, while a congestion toll is 14 justified when carriers are oligopolistic, from a first-best point of view a subsidy was 15 also justified as a means to fight against market power at the airline level and hence 13 16 reduce allocative inefficiencies. In the simple settings of one or two airports, both the

17 congestion effect and the market-power effect depended on a carrier’s flight share. But

18 in that case the airport share and the city-pair market share were the same. Brueckner

19 (2005) showed that, in a network setting, whilst the congestion tolls are airport-specific,

20 the subsidies required are city-pair specific. Hence, an airport regulator would need

21 to calculate appropriate airport-specific congestion tolls together with city-pair specific

22 subsides to obtain, finally, the optimal charge, which would be positive if the congestion

23 effect dominates the market-power effect. Brueckner argues that, since market-level

24 subsides are impractical to implement, only airport congestion tolls would be used,

25 an approach that would be welfare improving, yet not first-best, if congestion effects

26 dominate.

27 Now, both Oum et al. (1996) and Brueckner (2005) have assumed that the route

28 structure of airlines, that is, the way airlines move passengers between origins and

29 destinations, remain unchanged and is independent of the pricing practices of airports.

30 But, what would happen in the long run if the route structure is be changed? For

31 example, it has been often argued that economies of density drive the adoption of HS

32 networks. But if congestion at hubs is too important, airlines may decide to by-pass 14 33 them, offering direct connections in some city-pair markets. Would congestion pricing

34 affect the timing of such a decision? May airports use their pricing practices as a way to

35 compete for connecting passengers, that is, may they compete to become hubs? A model

36 including all these elements would be indeed very complicated and has, as far as we

37 know, not yet been proposed. However, there is one paper that, even though in a context

38 of non-congestible airports and a monopoly airline, does look at how airport pricing and

39 airline’s choice of route structure are related. Specifically, Pels et al. (1997) consider

40 a model with three non-congestible public airports (hence three OD city-pair markets) and a monopoly airline. Airport charges are directly made to passengers. Thus, the 41

43 13 On the other hand, we do not normally think of solving the market-power problem by subsidizing the firms, 44 for several good reasons. The subsidy may alternatively be interpreted as an imperfect proxy for some kind 45 of antitrust policy in its effect on price reduction. 46 14 For a paper related to this issue, see Basso and Jara-Diaz (2006).

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118 LEONARDO J. BASSO AND ANMING ZHANG

01 B 02 Fully connected Network (FC) 03 Hub and Spoke Route Structure (HS) 04 A 05

07 C 08 09 Figure 2 Possible Route Structures. 10

11 12 demands for airports and for the airline depend on both airfares and airport charges. 13 The airports and the monopoly airline play a simultaneous game in which each airport 14 chooses its per-passenger charge, while the airline chooses a route structure and its 15 airfares. The objective function of the airports is to maximize own social welfare (as in 16 the de-federalized case of Oum et al., 1996), which is measured as the integral of the 17 airport’s demand, subject to a budget constraint. The airline seeks to maximize its profit. 18 There are some key assumptions in the model, which are more easily explained using 19 Figure 2. 20

22 5.2 Possible Route Structures 23 First, it is assumed that node (airport) A has more passenger generating capacity. That 24 is, if airports’ and airline charges were zero, the demands in the AB and AC pairs would 25 be , while in the BC pair it would be , where <1. Second, consumers only care 26 about the monetary charges (from the airports and the airline) but would not care about 27 travel times (which are higher in a HS route structure) or whether they have to make 28 connections or not. Third, the marginal cost of carrying a passenger is constant and 29 equal across links; hence, in a HS route structure, a passenger traveling from B to C 30 would cost the airline 2c whilst with a FC route it would cost only c. Finally, if a link 31 is used, it has a fixed cost c0. Hence, a HS route structure is cheaper in terms of fixed 32 costs, as it only uses two links (vs. three links in a FC structure), but is more expensive 33 in term of operational costs. 34 Pels et al. (1997) show that, in this setup, if the airport charges are zero (or, if they are 35 equal but are chosen non-strategically, i.e., without considering what the airline does) a 36 HS route structure will be preferred by the monopoly airline if <, i.e. the demand in 37 the BC market is much smaller than the demands in the AB and AC markets. The limit 38 increases in both c and c0, and decreases in . Further, they show that the airline will always 39 choose to place its hub at the node with the highest level of demand, in this case, node A.15 40 When the airports choose their prices simultaneously with the airline’s choice of route 41 structure and airfares, Pels et al. show that the airport charges will increase in fares, 42 but the fares will decrease in airport charges. The “dynamics” of equilibrium would be 43

44 45 15 For more discussions on the choice of route structure, see, e.g., Oum et al. (1995), Hendricks et al. (1999), 46 Pels et al. (2000) and Jara-Diaz and Basso (2003).

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01 the monopoly airline, which is a profit maximizer, would increase its prices depressing 02 demands. Since the public airport must break even, it would raise its own charges, but 03 that would induce the airline to decrease its prices. This in turn would increase demand, 04 inducing a decrease in the airports’ charge, which in turn would induce the airlines 05 to increase price. Eventually, this loop may reach an equilibrium, although Pels et al. 06 show that non-existence of equilibrium is a possible outcome. Since analytical solution 07 of the equilibrium is unfeasible, they rely on a numerical simulation to extract more 08 conclusions. They found that, only if is small enough, the airline would choose a HS 09 route structure. The higher the , however, the better for the hub. More importantly, price 10 competition between the airports seems to have little effect on the airline’s choice of a 11 hub; the choice would still be made based on passenger generating capacity. Obviously, 12 one can foresee that the actual geographic position of the airports would be important 13 as well. A hub would not be placed really far away from all its spoke airports. But in 14 this model, distances, that is the topology of the network, does not play a role. This is 15 reasonable under the assumption that all airports are located fairly close or equidistant 16 from each other. 17

18 19 6 CONCLUSIONS AND FURTHER RESEARCH 20 21 Airport pricing has been widely analyzed in the economics literature. In this survey 22 paper, we have focused on analytical models of airport pricing from 1987 on. We have 23 grouped the models in the literature into two broad approaches. Roughly, the traditional 24 approach has used a classical partial equilibrium model where the demand for airports 25 depends on airport charges and on congestion costs of both passengers and airlines; the 26 airline market is not formally modeled, in several cases under the assumption that airline 27 competition is perfect and hence airport charges and delay costs are completely passed 28 to passengers. The vertical structure approach was motivated initially by the increasing 29 and acute congestion at major hub airports in the United States and around the world. 30 Since hub airports usually have only a few dominant airlines, the airline market there 31 is better characterized as oligopoly: air carriers may possess market power. Thus, the 32 airline market was considered in the analysis of airport pricing. Furthermore, the vertical 33 structure approach has recognized that airports provide an input for the airline market – 34 which is modeled as a rather simple oligopoly – and that it is the equilibrium of this 35 downstream market that determines the airports’ demand: the demand for airports is 36 therefore a derived demand. 37 The questions investigated with the two approaches have not perfectly overlapped. The 38 traditional approach has been used to analyze a variety of issues such as optimal capac- 39 ity investments, effect of concession revenues, privatization, efficiency of alternative 40 regulation mechanisms, cost recovery when capacity cannot be increased continuously, 41 and efficiency of weight-based airport charges. On the other hand, the vertical structure 42 approach has focused mainly on calculating the additional toll that airlines should be 43 charged to attain maximization of social welfare. It is only recently that vertical structure 44 models have been used to assess such issues as optimal capacity levels, or the effects 45 of privatization on airport charges. Drawing from results in Basso (2005), we indicated 46 here that abstracting from the airline market, as is done in the traditional approach, is a

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01 reasonable approximation only when airlines behave competitively, but it is not when 02 airlines have market power. In the latter case, the derived demand for the airport would 03 not be dependent only on its full price, as it is assumed in the traditional approach. As a 04 result, the integration of the airport demand with respect to the full price, which is said 05 to capture consumer surplus, would not adequately capture the surpluses of passengers 06 and airlines because market power and congestion effects preclude it. Therefore, in that 07 case, the function that is maximized in the first-best scenario would not correspond to 16 08 total social welfare. 09 The fact that the airline market cannot be ignored if airlines have market power 10 implies, on one hand, that future research would need to use vertical structure models if 11 the airline market structure is an important factor for the issues to be investigated. This 12 may include re-examination of some of the questions that have been addressed only with 13 the traditional approach, including, for example, the effect of concession revenues on 14 airport charges, the efficiency of regulation mechanisms for congested hub airports, and 15 congestion pricing with lumpy airport capacity. But on the practical side, the fact that 16 the airline market has to be included in the models is also bad news for managers of 17 public airports and regulators: to implement optimal decisions, the amount of information 18 required would be massive even in simple settings, which undoubtedly complicates the 19 problem. 20 In the models we have reviewed in this survey, authors have resorted to a number 21 of simplifications, which was the price to pay to preserve analytical tractability. In the 22 airline market of vertical structure models, two usual simplifications are the assumption 23 of fixed proportions and the assumption of symmetric airlines. The former was made 24 when the authors assumed, as constant, the product between aircraft size and load factor 25 (or both). Yet, it has been widely accepted that airlines enjoy what is called “economies 26 of traffic density” – decreasing average cost on nonstop connections – owing largely 27 to the economies of aircraft size. These economies are not considered under the fixed- 28 proportions assumption (which precludes the endogenous choice of aircraft types by 29 airlines). A variable-proportions case would arise because, if the charge per flight is too 30 high, airlines would have an incentive to change to larger airplanes, independently of 31 existing or exhausted economies of airplane size. So, with privatization for example, 32 not only capacities and traffic levels would be distorted downwards, but aircraft size 33 would be distorted as well. Modeling this effect is an interesting area of future research 34 albeit a complex one, as larger aircrafts imply smaller frequencies, which directly affects 17 35 congestion and demand through schedule delay costs. 36 Regarding the assumption of asymmetric airlines, certainly insights would be gained 37 if the analysis could be extended to the case of asymmetric airlines, as the model would 38 depict a more realistic case. Brueckner (2002, p. 1368) stated that “cost differences 39

40 41 16 This result in fact applies not only to airports but to any other types of transport terminal, or even railroad 42 tracks, since the situation is essentially the same. 17 43 Note that Raffarin (2004) is not an analysis of variable proportions case because, although she did considered different aircraft sizes, the airlines where not free to decide about their preferred aircraft size. Rather, the 44 aircraft size was exogenously given through a parameter, which thus showed up in the final pricing rules of 45 the airport. Also, in her model congestion did not directly affect passengers or airlines but was an external 46 cost to be minimized by the airport authority and capacity was fixed.

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01 across firms may not be a useful source of asymmetry, however, because a planner would 02 not allow high-cost firms to operate at the social optimum.” In Basso (2005) and Zhang 03 and Zhang (2006), however, there was no social planner but rather managers of public 04 airports maximizing social welfare, who probably would not have the power to preclude 05 less efficient airlines to operate. But they did not consider asymmetries. It seems, to us, 06 that characterizing the properties for the case of asymmetric airlines would be unfeasible 07 analytically; instead, numerical simulations would be required. Pels and Verhoef (2004) 08 did present some numerical simulation results for the case of an asymmetric duopoly 09 (see Table 2 for a description of their setting). 10 The papers in Section 3 have looked at either a single airport in isolation or, at most, 11 round-trip travel between two airports. In the latter case, the airports have complementary 12 demands; consequently, public airports that are priced independently would not achieve

13 a first-best outcome (Pels and Verhoef, 2004), and separate private airports would end up

14 with a horizontal double marginalization (Basso, 2005). However, airport networks are

15 more complex than that; and on this subject, the papers presented in Section 5 represent

16 good progress in understanding the main issues. Nevertheless, we believe that there is

17 still much work to do. In Oum et al. (1996) and Brueckner (2005) there were no route

18 structure decisions on the part of airlines, but it is through route structure decisions that

19 airports may actually compete: they would be competing for connecting passengers. On

20 the other hand, although considering route structure decisions, Pels et al. (1997) do not

21 include congestion, capacity choices, or airline competition. Further work on the pricing

22 of network airports – including effects of privatization and regulation mechanisms – is,

23 in our view, a clear line of future work.

24 A related aspect is geographic competition: airports competing for costumers in the

25 same origin, i.e., with overlapping catchment areas, as in the case of New York and San

26 Francisco Bay Area. There has been some empirical work on this issue (e.g., Ishii et al.,

27 2005, and the references cited there), but not too much work on the analytical side.

28 Some papers have looked at competition between congestible Bertrand facilities (e.g.,

29 De Borger and Van Dender, 2006) but they overlooked the intermediate carrier market in

30 vertical structures discussed above. A simple model of geographic competition between

31 two airport-airline structures is Gillen and Morrison (2003). But they considered only

32 the case of one airline per airport and the joint airport–airline profit maximization, and they did not consider the issues of airport congestion and airport capacity choices. We 33 think that competition in multiple-airport regions with congestion is another interesting 34 area of future research.18 35 Another important aspect is the issue of peak-load pricing, in addition to just con- 36 gestion pricing. Most of the models we have reviewed are about congestion pricing 37 rather than peak-load pricing, in the sense that even if there is more than one period 38 in those models, the demands between periods are not interdependent. Hence, the only 39 way to fight against excess usage is to dampen the demands. When the periods are 40 interdependent, however, pricing can be used not only to dampen the demands, but also 41 to redistribute consumers and flights across different periods, “flattening” the demand 42

44 18 As this survey was being completed, a paper dealing with the specific issue of geographic competition was 45 accepted for publication. Time precluded the presentation of the main results in this review. For details see 46 Basso and Zhang (2006a).

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122 LEONARDO J. BASSO AND ANMING ZHANG

01 curve – the case of peak-load pricing. Brueckner (2002) allowed for endogenous sorting 02 to peak and off-peak periods, but the sorting was done mainly through airlines’ decisions. 03 If the airlines use peak-load pricing, then that would deliver a different demand pattern 04 to the airport, which would probably also have peak and off-peak periods. The airport 05 would then have an incentive to choose prices for its own peak and off-peak periods, 06 probably using peak-load pricing as well, in order to maximize its objective function. 07 The objective function would be dependent on the type of ownership and regulation. 08 Hence, we would be in a situation of sequential peak-load pricing, which represents 09 particularly well the case of airports and airlines (Basso and Zhang, 2006b). 10 We have highlighted some of the issues that we think should be examined in the 11 future, but perhaps one of the most important aspects of future research has to do with 12 actual policies. It is seldom true that airports are priced as in a system, and it is seldom 13 true that airport managers have access to all the information that they would need to do 14 what is best. Hence, how should public airports be priced when they are not in a system, 15 and when information is incomplete? And given this, what are the costs and gains of 16 airport privatization, and what would be a good and feasible regulation mechanism for 17 privatized airports? Investigating these questions will advance our understanding of the 18 subject and produce useful guidance to policy formulations. 19

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01 Chapter No: 04 02

03 Query No Query

04 AU1: Please update Basso and Zhang (2006a). 05 AU2: Please note that Jones, Viehoff, and Marks (1993) has been 06 changed to Jones et al. (1991) as per the list. Is this OK? 07

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