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Airline pricing and airport charges in hub-spoke networks with congestion Ming Hsin Lin* and Yimin Zhang** October 6, 2011 Abstract This article investigates airline pricing and airport congestion charges in hub-spoke networks. When a public hub airport and two public spoke (local) airports independently levy their charges, airlines will eventually set a ticket price that overcharges the passengers for congestion delay cost and overcompensates for airline markups. Privatizing only local airports will always lead to more overcharge, whereas privatizing only the hub airport or all airports could result in lesser overcharge if the network markets are competitive. The degree of overcharge under a private hub and public local airports is always lesser than that under a public hub and private local airports, implying that privatizing a hub airport could yield higher social welfare than privatizing a local airport. Furthermore, investigation on compensation for airline markups also finds that privatizing a hub airport is preferable to privatizing a local airport. These findings have policy implications for airport privatization.

JEL: L93; L30; H20 Keywords: hub-spoke network; airline pricing; congestion charges; airport privatization

*

Faculty of Economics, Osaka University of Economics. 2-2-8 Osumi, Higashiyodogawa-ku, Osaka 533-8533, Japan. Fax: +81-6-6328-1825 E-mail: [email protected] ** China Europe International Business School. 699 Hongfeng Road, Pudong, Shanghai, China 201206. Fax: +8621-2890-5620E-mail: [email protected] 1

Electronic copy available at: http://ssrn.com/abstract=1939745

1. Introduction Airport congestion has become an essential concern in many regions with a rapid growth in air transport demand. Some airports have adopted congestion pricing based on the conventional economic wisdom. Several recent works, however, pointed out that congestion pricing has no (or only partial) place at an airport when carriers have market power, because carriers themselves will internalize congestion (see Brueckner 2002; Pel and Verhoef 2004; Brueckner 2005; Zhang and Zhang 2006, among others). On the other hand, one important aspect of air transport business is the vertical structure with airports in the upstream market and airlines in the downstream market. Therefore, as arguing airports’ congestion pricing, the interaction with the carriers’ pricing is relevantly important. Moreover, the growing adoption of hub-spoke airline networks, doubtlessly, deepens the congestion problem for not only hub airports but also local (spoke) airports.1 In light of these air transport characteristic, it is meaningful to investigate the issue on a network basis involving multiple city pair markets. Another important aspect is privatization of airports. Although airports around the world were traditionally owned and operated by notional or local governments,

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Subsequent to airline deregulation, air carriers have transformed their networks into the hub-spoke type for cost saving and strategic reasons. The economic efficiency of hub-spoke networks may generate from economies of traffic density on cost side and/or from flight frequencies effects on demand side. 2

Electronic copy available at: http://ssrn.com/abstract=1939745

numerous countries have taken measures to privatize their airports partially or wholly for purposes of improving the economic efficiency (see Oum et al. 2008).2 In the present study, our analytical concerns are on the different types (i.e., hub or local airports) of fully privatized airports in hub-spoke networks. In the previous studies, Brueckner (2002), Zhang and Zhang (2006) and Brueckner and Verhoef (2010) focused on a single-airport case, where destination airports are ignored. For models with a network of airports, Pels and Verhoef (2004) considered two nodes (airports) where two airlines and passengers suffer congestion at both airports. Under a parametric setting, they investigated congestion tolls that can be determined either by a single regulator for both airports, or by two (national or regional) regulators, each regulating a specific airport. Pels and Verhoef (2004) concluded that non-cooperation between independent airport regulators may lead to welfare losses as compared with the case when no congestion tolls are levied. Brueckner (2005) constructed a network containing two hub airports, each serves a hub-spoke network carrier, to argue the socially optimal airport charges determined by one single public authority. Flores-Fillol (2010) considered a simple network where a hub airport links two spoke airports, to address the interaction between flight frequency and aircraft size,

2

For ownership and governance structure of worldwide airports, see Table 1 in Oum et al.(2006). 3

under duopolistic network carriers and specified functions. In this article, we study the implications of airline pricing and airport charges in a hub-spoke network with one hub linking two spoke (local) airports. We consider various airport charges of public or private authorities in either hub or local airports. There are N Cournot-type carriers who service the three markets: two local markets and one connecting market, and congestion occurred in all three airports. Under quite general setting we first find that, while the welfare-maximizing hub and local airports independently levy the optimal airport charge in the first stage, the passengers will eventually pay a ticket price that overcharges for the congestion delay cost and overcompensates for airline markups in the second stage. Second, our analysis of mixed ownerships of the hub and local airports find that the degree of overcharge for congestion delay cost on passengers is lesser under a private hub and public local airports than that under a public hub and private local airports. This finding has important implication to airport privatization scheme: privatizing a hub airport could yield higher social welfare than privatizing a local airport. Moreover, as compared with all public airports case, privatizing only the local airport will always lead to more overcharge, whereas privatize only the hub airport or privatize both airports could results in lesser overcharge if the number of network carriers is large (the airline

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market is more competitive). We further find that, the rebates to passengers contained in airport charges under a private hub and public local airports just compensate for airline markups whereas the other combinations of airport ownerships over/under compensate for airline markups. This finding also suggests that privatizing a hub airport is preferable to privatizing a local airport. The remainder of the study is organized as follows: Section 2 presents the model of a hub-spoke network with congestion. Section 3 examines airlines’ pricing. Sections 4 and 5 derive optimal airport charges for public and private airports and examine the resulting airlines’ ticket price. Section 6 contains the concluding remarks. 2. The Model

Figure 1 a simple hub-spoke network Let us consider a hub-spoke airline network where the hub airport H links two local airports A and B. The airports service N symmetric carriers, each of them is a hub-spoke 5

network operator (i.e., operates two direct flights to service the three city-pair markets). Let π‘„π‘š = π‘„π‘š (πœŒπ‘š ), π‘š = 𝐴𝐻, 𝐡𝐻, 𝐴𝐡 denote the aggregate demand in city-pair market π‘š, where πœŒπ‘š represents the β€œfull price” of travel by a passenger. The full price of markets AH and BH are defined as (1)

𝜌𝐴𝐻 = 𝑃𝐴𝐻 + π·π‘Ž (πΉπ‘Ž ) + 𝐷𝑕 (πΉπ‘Ž + 𝐹𝑏 )

(2)

𝜌𝐡𝐻 = 𝑃𝐡𝐻 + 𝐷𝑏 (𝐹𝑏 ) + 𝐷𝑕 (𝐹𝑏 + πΉπ‘Ž )

In words, 𝜌𝐴𝐻 is the sum of ticket price 𝑃𝐴𝐻 and costs of congestion delay occurred in local airport A (denoted by π·π‘Ž ) and in hub airport H (denoted by 𝐷𝑕 ). The function π·π‘Ž depends on the total frequencies on spoke AH, πΉπ‘Ž , while 𝐷𝑕 also depends on the total frequencies on spoke BH, 𝐹𝑏 . Similar notations apply to market BH. The full price of market AB is defined as (3)

𝜌𝐴𝐡 = 𝑃𝐴𝐡 + π·π‘Ž (πΉπ‘Ž ) + 2𝐷𝑕 (πΉπ‘Ž + 𝐹𝑏 ) + 𝐷𝑏 (𝐹𝑏 )

Notice that 2𝐷𝑕 (πΉπ‘Ž + 𝐹𝑏 ) in (3) comes from the fact that the transfer passenger AB needs two flight movements (one landing and one subsequent takeoff) at hub airport and, therefore, suffers from two congestion delays at the hub. We assume general properties of congestion delay cost 𝐷𝑙 , (𝑙 = π‘Ž, 𝑏, β„Ž) as follows: (4)

𝐷𝑙 = 𝐷(𝐹𝑙 ),

πœ•π·π‘™ πœ•πΉπ‘™

≑ 𝐷𝑙′ > 0,

πœ• 2 𝐷𝑙 πœ•πΉπ‘™2

≑ 𝐷𝑙′′ > 0.

There are N symmetric network carriers competing in Cournot fashion. For simplicity,

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we assume that all carriers use a single type of aircraft with constant number of seats per flight denoted by 𝑠. A representative carrier, airline 𝑖, operates two direct flights AH and BH with frequencies π‘“π‘–π‘Ž and 𝑓𝑖𝑏 , to provide nonstop services with quantities (total traffic) π‘žπ‘–π‘Ž and π‘žπ‘–π‘ in markets AH and BH and one-stop service with quantity π‘žπ‘–π‘œ in market AB. By noting that connecting passengers use both spokes AH and BH, we have the following relationships: (π‘žπ‘–π‘Ž + π‘žπ‘–π‘œ ) = 𝑠 π‘“π‘–π‘Ž and (π‘žπ‘–π‘ + π‘žπ‘–π‘œ ) = 𝑠 𝑓𝑖𝑏 . Given the fixed 𝑠, once airline 𝑖’s strategic variables, π‘žπ‘–π‘Ž , π‘žπ‘–π‘ and π‘žπ‘–π‘œ are decided, the frequencies π‘“π‘–π‘Ž and 𝑓𝑖𝑏 are determined accordingly. The aggregate demand of the three markets are 𝑁 𝑁 given by 𝑄𝐴𝐻 = βˆ‘π‘ 𝑖 π‘žπ‘–π‘Ž , 𝑄𝐡𝐻 = βˆ‘π‘– π‘žπ‘–π‘ and 𝑄𝐴𝐡 = βˆ‘π‘– π‘žπ‘–π‘œ . The total frequencies of 𝑁 spoke AH are πΉπ‘Ž = βˆ‘π‘ 𝑖 π‘“π‘–π‘Ž = βˆ‘π‘– (π‘žπ‘–π‘Ž + π‘žπ‘–π‘œ )/𝑠 = (𝑄𝐴𝐻 + 𝑄𝐴𝐡 )/𝑠 and those of spoke 𝑁 BH are 𝐹𝑏 = βˆ‘π‘ 𝑖 𝑓𝑖𝑏 = βˆ‘π‘– (π‘žπ‘–π‘ + π‘žπ‘–π‘œ )/𝑠 = (𝑄𝐡𝐻 + 𝑄𝐴𝐡 )/𝑠.

Airline 𝑖’s total costs for operating its hub-spoke network are the sum of πΆπ‘Ž = πœƒ π‘“π‘–π‘Ž + 𝜏 (π‘žπ‘–π‘Ž + π‘žπ‘–π‘œ ) and 𝐢𝑏 = πœƒ 𝑓𝑖𝑏 + 𝜏 (π‘žπ‘–π‘ + π‘žπ‘–π‘œ ), or, (5)

πœƒ

βˆ‘π‘˜ πœƒ,(π‘žπ‘–π‘˜ + π‘žπ‘–π‘œ )/𝑠- + βˆ‘π‘˜ 𝜏 (π‘žπ‘–π‘˜ + π‘žπ‘–π‘œ ) = βˆ‘π‘˜ . + 𝜏/ (π‘žπ‘–π‘˜ + π‘žπ‘–π‘œ ) , π‘˜ = π‘Ž, 𝑏, 𝑠

where πœƒ is the operating costs per flight (with a constant aircraft size 𝑠) and 𝜏 is the πœƒ

operating costs per passenger. Let 𝑑 ≑ . 𝑠 + 𝜏/ represent airline 𝑖's total operating cost per passenger.

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Airlines have to pay airport charges to the three airports. We assume that the airport charges are weight based and are proportional to 𝑠. Let πœ‡π‘• 𝑠 denote the hub airport’s charge per aircraft movement, πœ‡π‘˜ 𝑠 (π‘˜ = π‘Ž, 𝑏) denote that of a local airport. Using (π‘žπ‘–π‘Ž + π‘žπ‘–π‘œ ) = 𝑠 π‘“π‘–π‘Ž and (π‘žπ‘–π‘ + π‘žπ‘–π‘œ ) = 𝑠 𝑓𝑖𝑏 , we can write airline 𝑖’s profit function as (6)

πœ‹π‘–π‘Žπ‘–π‘Ÿπ‘™π‘–π‘›π‘’ ≑ πœ‹π‘– = 𝑃𝐴𝐻 π‘žπ‘–π‘Ž + 𝑃𝐡𝐻 π‘žπ‘–π‘ + 𝑃𝐴𝐡 π‘žπ‘–π‘œ βˆ’ βˆ‘π‘˜(πœ‡π‘˜ + πœ‡π‘• )(π‘žπ‘–π‘˜ + π‘žπ‘–π‘œ ) βˆ’ βˆ‘π‘˜ 𝑑(π‘žπ‘–π‘˜ + π‘žπ‘–π‘œ ) , π‘˜ = π‘Ž, 𝑏

For simplicity, we further assume that the two spoke markets and airports A and B are symmetric. By these symmetries, the full price of a local traffic (spoke) market with nonstop services can be written as (7)

𝜌 = 𝑃 + 𝐷(𝐹) + 𝐷𝑕 (2𝐹)

Similarly, the full price of the market AB with one-stop services can be written as (8)

πœŒπ‘œ = π‘ƒπ‘œ + 2𝐷(𝐹) + 2𝐷𝑕 (2𝐹)

3. Airline’s strategic decision Giving the symmetry assumptions and the definition of full price, the profit function of airline 𝑖 can be simplified into (9)

πœ‹π‘– = 2(𝜌 βˆ’ 𝐷 βˆ’ 𝐷𝑕 )π‘žπ‘– + (πœŒπ‘œ βˆ’ 2𝐷 βˆ’ 2𝐷𝑕 )π‘žπ‘–π‘œ βˆ’ 2(𝑑 + πœ‡ + πœ‡π‘• )(π‘žπ‘– + π‘žπ‘–π‘œ ),

where π‘žπ‘–π‘Ž = π‘žπ‘–π‘ ≑ π‘žπ‘– . The first-order conditions of airline 𝑖’s profit maximization problem are

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πœ•πœ‹π‘–

(10)

= 2,πœŒβ€² π‘žπ‘– + (𝜌 βˆ’ 𝐷 βˆ’ 𝐷𝑕 ) βˆ’ (𝐷′ + 𝐷𝑕′ )(π‘žπ‘– + π‘žπ‘–π‘œ ) βˆ’ (𝑑 + πœ‡ + πœ‡π‘• )- = 0, βˆ€π‘–

πœ•π‘žπ‘– πœ•πœ‹π‘–

(11)

πœ•π‘žπ‘–π‘œ

= πœŒπ‘œβ€² π‘žπ‘–π‘œ + (πœŒπ‘œ βˆ’ 2𝐷 βˆ’ 2𝐷𝑕 ) βˆ’ 2(𝐷′ + 𝐷𝑕′ )(π‘žπ‘– + π‘žπ‘–π‘œ ) βˆ’ 2(𝑑 + πœ‡ + πœ‡π‘• ) =

0, βˆ€π‘–. The second-order conditions are πœ•2 πœ‹

(12)

πœ•π‘žπ‘– πœ•π‘žπ‘–

πœ•2 πœ‹ πœ•π‘žπ‘–π‘œ πœ•π‘žπ‘–π‘œ πœ•2 πœ‹

= 2(πœŒβ€²β€² π‘žπ‘– + 2πœŒβ€² ) βˆ’ 4(𝐷′ + 𝐷𝑕′ ) βˆ’ 2(𝐷′′ + 𝐷𝑕′′ )(π‘žπ‘– + π‘žπ‘–π‘œ ) < 0,

= (πœŒπ‘œβ€²β€² π‘žπ‘–π‘œ + 2πœŒπ‘œβ€² ) βˆ’ 4(𝐷′ + 𝐷𝑕′ ) βˆ’ 2((𝐷′′ + 𝐷𝑕′′ )(π‘žπ‘– + π‘žπ‘–π‘œ )) < 0, πœ•2 πœ‹

πœ•π‘žπ‘– πœ•π‘žπ‘–π‘œ

= πœ•π‘ž

πœ•2 πœ‹

πœ•2 πœ‹

π‘–π‘œ πœ•π‘žπ‘–

= βˆ’4(𝐷′ + 𝐷𝑕′ ) βˆ’ 2(𝐷′′ + 𝐷𝑕′′ )(π‘žπ‘– + π‘žπ‘–π‘œ ), πœ•2 πœ‹

πœ•π‘žπ‘– πœ•π‘žπ‘– πœ•π‘žπ‘–π‘œ πœ•π‘žπ‘–π‘œ

βˆ’ πœ•π‘ž πœ•π‘ž 𝑖

πœ•2 πœ‹ π‘–π‘œ

πœ•π‘žπ‘–π‘œ πœ•π‘žπ‘–

> 0, βˆ€π‘–.

Following the standard practice in models of quantity competition (e.g. Tirole 1988) we assume that a carrier’s marginal profit declines when another carrier’s output rises, implying that the carriers’ outputs are β€œstrategic substitutes” (Bulow et al. 1985). We further assume that the equilibrium is locally, strictly stable. Then, differentiating both sides of (10)-(11) with respect to πœ‡ and πœ‡π‘• , respectively, and solving the equations gives the following comparative-static effects of airport charges. (13) (14) (15) (16)

πœ•π‘„ πœ•πœ‡

= 𝑁((πœŒπ‘œβ€²β€² π‘žπ‘œ + 2πœŒπ‘œβ€² ) + (𝑁 βˆ’ 1)(πœŒπ‘œβ€²β€² π‘žπ‘œ + πœŒπ‘œβ€² ))π›¬βˆ’1 < 0,

πœ•π‘„π‘œ πœ•πœ‡ πœ•π‘„ πœ•πœ‡β„Ž πœ•π‘„π‘œ πœ•πœ‡β„Ž

= 2𝑁((πœŒβ€²β€² π‘ž + 2πœŒβ€² ) + (𝑁 βˆ’ 1)(πœŒβ€²β€² π‘ž + πœŒβ€² ))π›¬βˆ’1 < 0, = 2𝑁((πœŒπ‘œβ€²β€² π‘žπ‘œ + 2πœŒπ‘œβ€² ) + (𝑁 βˆ’ 1)(πœŒπ‘œβ€²β€² π‘žπ‘œ + πœŒπ‘œβ€² ))π›¬βˆ’1 < 0, = 4𝑁((πœŒβ€²β€² π‘ž + 2πœŒβ€² ) + (𝑁 βˆ’ 1)(πœŒβ€²β€² π‘ž + πœŒβ€² ))π›¬βˆ’1 < 0.

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For convenience, we define the two common parts in (13)-(16), each is the slope of airlines’ marginal revenue with a negative value, as (πœŒβ€²β€² π‘ž + 2πœŒβ€² ) + (𝑁 βˆ’ 1)(πœŒβ€²β€² π‘ž + πœŒβ€² ) ≑ 𝑋 and (πœŒπ‘œβ€²β€² π‘žπ‘œ + 2πœŒπ‘œβ€² ) + (𝑁 βˆ’ 1)(πœŒπ‘œβ€²β€² π‘žπ‘œ + πœŒπ‘œβ€² ) ≑ π‘‹π‘œ . The inequalities in (13)-(16) hold by the assumption of local strict stability, that is 𝛬 = 2π‘‹π‘‹π‘œ βˆ’ 2(2𝑋 + π‘‹π‘œ )((1 + 𝑁)(𝐷′ + 𝐷𝑕′ ) + 𝑁(𝐷 β€² β€² + 𝐷𝑕′′ + 𝐺 β€²β€² )(π‘ž + π‘žπ‘œ )) > 0. These results show that aggregate (equilibrium) outputs decrease in airport charges. 4. Airport charge for public airports Generally, airport operating costs have two components. One is the runway operating cost, which is flight based, and the other is terminal operating cost, which depends on 𝑓

number of passengers handled. For the hub airport, let 𝑐𝑕 denote its cost of runway operation per flight and π‘π‘•π‘ž of its terminal operating cost per passenger. Then, the total 𝑓

operating cost of the hub airport can be written as 𝑐𝑕 (πΉπ‘Ž + 𝐹𝑏 ) + π‘π‘•π‘ž (𝑄𝐴𝐻 + 𝑄𝐡𝐻 + 𝑐

𝑓

2𝑄𝐴𝐡 ) = 𝑐𝑕 ( 2𝑄 + 2π‘„π‘œ ), where 𝑄𝐴𝐻 = 𝑄𝐡𝐻 ≑ 𝑄 , 𝑄𝐴𝐡 ≑ π‘„π‘œ and 𝑐𝑕 ≑ ( π‘ β„Ž + π‘π‘•π‘ž ) representing its total operating cost per passenger. Similar notations apply to costs of local airports by dropping the subscript "β„Ž". The profit of hub airport H can be written as: (17)

Π𝑕 = 2(πœ‡π‘• βˆ’ 𝑐𝑕 )(𝑄 + π‘„π‘œ )

Similarly, the profit of local airport 𝑗 (𝑗 = 𝐴, 𝐡) can be written as:

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(18)

𝛱𝑗 = (πœ‡ βˆ’ 𝑐)(𝑄 + π‘„π‘œ ), 𝑐𝑓

where c ≑ . 𝑠 + 𝑐 π‘ž / represent local airport 𝑗's total operating cost per passenger. 4.1. Welfare-maximizing hub airport charge The public hub airport has welfare concerns consisting of its users’ (i.e., airlines’ and passengers’) surplus and its own profits. Therefore, the objective of the welfare-maximizing hub airport can be formulated as follows: (19)

𝑄

𝑄

π‘šπ‘Žπ‘₯πœ‡β„Ž π‘Šπ‘• = 22 ∫0 𝜌(πœ‰)π‘‘πœ‰ βˆ’ 2 𝜌 𝑄 3 + 2∫0 π‘œ πœŒπ‘œ (πœ‰)π‘‘πœ‰ βˆ’ πœŒπ‘œ π‘„π‘œ 3 +*2 (𝜌 βˆ’ 𝐷 βˆ’

𝐷𝑕 ) 𝑄 + (πœŒπ‘œ βˆ’ 2𝐷 βˆ’ 2𝐷𝑕 )π‘„π‘œ βˆ’ 2(𝑑 + πœ‡ + πœ‡π‘• ) (𝑄 + π‘„π‘œ )+ + *2(πœ‡π‘• βˆ’ 𝑐𝑕 )(𝑄 + π‘„π‘œ )+. In (19), the first (the second) braced terms are the consumer surplus of the two local markets AH and BH (the connecting market AB). The third braced terms are the total profits of all airlines and the remainders are the hub airport’s profits. The function π‘Šπ‘• can be simplified as (20)

𝑄

𝑄

π‘Šπ‘• = 2 ∫0 𝜌(πœ‰)π‘‘πœ‰ + ∫0 π‘œ πœŒπ‘œ (πœ‰)π‘‘πœ‰ βˆ’ 2 (𝐷 + 𝐷𝑕 )(𝑄 + π‘„π‘œ ) βˆ’ 2 (𝑑 + 𝑐𝑕 +

πœ‡)(𝑄 + π‘„π‘œ ). The first-order conditions for the optimal hub airport charge is πœ•π‘Šβ„Ž πœ•π‘„π‘œ πœ•π‘„π‘œ πœ•πœ‡β„Ž

/ = 0. Deriving the values of

πœ•π‘Šβ„Ž πœ•π‘„

and

conditions (10)-(11) yield

11

πœ•π‘Šβ„Ž πœ•π‘„π‘œ

πœ•π‘Šβ„Ž πœ•πœ‡β„Ž

=.

πœ•π‘Šβ„Ž πœ•π‘„ πœ•π‘„ πœ•πœ‡β„Ž

+

and using the airlines’ first-order

πœ•π‘Šβ„Ž

(21)

πœ•π‘„ πœ•π‘Šβ„Ž

(22)

πœ•π‘„π‘œ

= 2 .βˆ’πœŒβ€² π‘ž βˆ’ .

π‘βˆ’1 𝑁

/ (𝐷′ + 𝐷𝑕′ )(𝑄 + π‘„π‘œ ) + πœ‡π‘• βˆ’ 𝑐𝑕 /,

π‘βˆ’1

= .βˆ’πœŒπ‘œβ€² π‘žπ‘œ βˆ’ 2 .

𝑁

/ (𝐷′ + 𝐷𝑕′ )(𝑄 + π‘„π‘œ ) + 2πœ‡π‘• βˆ’ 2𝑐𝑕 /.

Therefore, πœ•π‘Šβ„Ž

(23)

πœ•πœ‡β„Ž

πœ•π‘„

= πœ•πœ‡ 2 .βˆ’πœŒβ€² π‘ž βˆ’ . β„Ž

π‘βˆ’1 𝑁

πœ•π‘„

/ (𝐷′ + 𝐷𝑕′ )(𝑄 + π‘„π‘œ ) + πœ‡π‘• βˆ’ 𝑐𝑕 / + πœ•πœ‡π‘œ .βˆ’πœŒπ‘œβ€² π‘žπ‘œ βˆ’ β„Ž

π‘βˆ’1

2.

𝑁

/ (𝐷′ + 𝐷𝑕′ )(𝑄 + π‘„π‘œ ) + 2πœ‡π‘• βˆ’ 2𝑐𝑕 / = 0.

Solving (23) for πœ‡π‘• and using (15)-(16), we have the optimal rule for the hub airport’s charge as follows: (24)

πœ‡π‘•π‘π‘’π‘ = 𝑐𝑕 +

Let Ξ΅ ≑ βˆ’

𝑑𝑄/𝑄 π‘‘πœŒ/𝜌

πœŒπ‘œβ€² π‘žπ‘œ 𝑋+πœŒβ€² π‘žπ‘‹π‘œ 2𝑋+π‘‹π‘œ

and πœ€π‘œ ≑ βˆ’

+.

π‘‘π‘„π‘œ /π‘„π‘œ π‘‘πœŒπ‘œ /πœŒπ‘œ

π‘βˆ’1 𝑁

/ (𝐷′ + 𝐷𝑕′ )(𝑄 + π‘„π‘œ ). 1𝜌

. We have πœŒβ€² π‘ž = βˆ’ .

π‘πœ€

1 πœŒπ‘œ

/ and πœŒπ‘œβ€² π‘žπ‘œ = βˆ’ .

𝑁 πœ€π‘œ

/.

Then, (24) can be rewritten as (25)

1

1

𝜌

2𝑋

𝜌

𝑋

π‘œ β€² β€² πœ‡π‘•π‘π‘’π‘ = 𝑐𝑕 + .1 0 π‘œ. / + πœ€ .2𝑋+𝑋 /1. ⏟ βˆ’ 𝑁/ (𝐷 + 𝐷𝑕 )(𝑄 + π‘„π‘œ ) βˆ’ 𝑁 ⏟ 2πœ€π‘œ 2𝑋+π‘‹π‘œ π‘œ

π‘π‘œπ‘›π‘”π‘’π‘ π‘‘π‘–π‘œπ‘› π‘‘π‘’π‘™π‘Žπ‘¦ π‘π‘œπ‘ π‘‘

π‘Žπ‘–π‘Ÿπ‘™π‘–π‘›π‘’ π‘šπ‘Žπ‘Ÿπ‘˜π‘’π‘

This optimal airport charge is consistent with Brueckner (2002), Pels and Verhoef (2004), and Zhang and Zhang’s (2006) results. Equation (25) has the clear interpretation that the hub airport charge is equal to the sum of the hub airport's total operating cost per passenger and the residual share of congestion delay costs (net of internalized 1

portion .𝑁/ by the airlines) in the hub-spoke network, minus a rebate term reflecting carriers’ market power in both local markets and the connecting market. 4.2. Welfare-maximizing local airport charge 12

A local airport 𝑗 (𝑗 = 𝐴, 𝐡) services the 𝑗H and AB passengers. Accordingly, the objective of a public local airport 𝑗 can be formulated as follows: maxπœ‡π‘— π‘Šπ‘— =

(26) 𝑄

𝑄

2∫0 𝑗 πœŒπ‘— (πœ‰)π‘‘πœ‰ βˆ’ πœŒπ‘— 𝑄𝑗 + [πœŒπ‘— βˆ’ (𝐷𝑗 + 𝐷𝑕 ) βˆ’ (𝑑 + πœ‡π‘— + πœ‡π‘• )]𝑄𝑗 3 + 2∫0 π‘œ πœŒπ‘œ (πœ‰)π‘‘πœ‰ βˆ’ πœŒπ‘œ π‘„π‘œ + [πœŒπ‘œ βˆ’ (𝐷𝑗 + 2𝐷𝑕 + π·π‘˜ ) βˆ’ (2𝑑 + πœ‡π‘— + 2πœ‡π‘• + πœ‡π‘˜ )]π‘„π‘œ 3 + (πœ‡π‘— βˆ’ 𝑐𝑗 )(𝑄𝑗 + π‘„π‘œ ). or, after simplification: 𝑄

𝑄

maxπœ‡π‘— π‘Šπ‘— = ∫0 𝑗 πœŒπ‘— (πœ‰)π‘‘πœ‰ + ∫0 π‘œ πœŒπ‘œ (πœ‰)π‘‘πœ‰ βˆ’ (𝐷𝑗 + 𝐷𝑕 )𝑄𝑗 βˆ’ (𝐷𝑗 + π·π‘˜ +

(27)

2𝐷𝑕 )π‘„π‘œ βˆ’ (𝑑 + 𝑐𝑗 + πœ‡π‘• )𝑄𝑗 βˆ’ (2𝑑 + 𝑐𝑗 + 2πœ‡π‘• + πœ‡π‘˜ )π‘„π‘œ . The first-order condition for optimality of local airport 𝑗’s charge is πœ•π‘Šπ‘— πœ•π‘„π‘œ πœ•π‘„π‘œ πœ•πœ‡π‘—

(28)

πœ•π‘Šπ‘— πœ•πœ‡π‘—

πœ•π‘Š πœ•π‘„

= ( πœ•π‘„ 𝑗 πœ•πœ‡π‘— + 𝑗

𝑗

) = 0. Using the similar approach for the hub airport, we obtain πœ•π‘Šπ‘— πœ•πœ‡π‘—

π‘βˆ’1

= 2βˆ’πœŒβ€² π‘ž βˆ’ .

𝑁

πœ•π‘„

/ (𝐷′ + 𝐷𝑕′ )(𝑄 + π‘„π‘œ ) βˆ’ 𝐷𝑕′ π‘„π‘œ + πœ‡π‘— βˆ’ 𝑐𝑗 3 πœ•πœ‡ +

π‘βˆ’2

πœ•π‘„π‘œ

𝑁

πœ•πœ‡

2βˆ’πœŒπ‘œβ€² π‘žπ‘œ βˆ’ .

/ (𝐷′ + 𝐷𝑕′ )(𝑄 + π‘„π‘œ ) βˆ’ (𝐷′ + 𝐷𝑕′ )π‘„π‘œ + πœ‡π‘— βˆ’ 𝑐𝑗 3

= 0.

Solving (28) for πœ‡, and using (13)-(14), we have the optimal charge for a local airport as follows. (29)

π‘βˆ’1

πœ‡ 𝑝𝑒𝑏 = 𝑐𝑗 + .

𝑁

2𝑋

π‘œ

(π‘βˆ’1)π‘„π‘œ βˆ’π‘„

2𝑋

.2𝑋+𝑋 / (𝐷′ + 𝐷𝑕′ ) . π‘œ

𝑋

π‘œ / (𝐷′ + 𝐷𝑕′ )(𝑄 + π‘„π‘œ ) + πœŒπ‘œβ€² π‘žπ‘œ .2𝑋+𝑋 / + πœŒβ€² π‘ž .2𝑋+𝑋 /+

𝑁

𝑋

π‘œ / + .2𝑋+𝑋 / 𝐷𝑕′ π‘„π‘œ , π‘œ

or equivalently,

13

π‘œ

(30)

1

1 𝜌

2𝑋

𝜌

𝑋

π‘œ β€² β€² πœ‡ 𝑝𝑒𝑏 = 𝑐𝑗 + .1 0 π‘œ. / + πœ€ .2𝑋+𝑋 /1 + ⏟ βˆ’ 𝑁/ (𝐷 + 𝐷𝑕 )(𝑄 + π‘„π‘œ ) βˆ’ 𝑁 ⏟ πœ€π‘œ 2𝑋+π‘‹π‘œ π‘œ

π‘π‘œπ‘›π‘”π‘’π‘ π‘‘π‘–π‘œπ‘› π‘‘π‘’π‘™π‘Žπ‘¦ π‘π‘œπ‘ π‘‘ (π‘βˆ’1)π‘„π‘œ βˆ’π‘„

2𝑋

.2𝑋+𝑋 / (𝐷′ + 𝐷𝑕′ ) . π‘œ

𝑁

π‘Žπ‘–π‘Ÿπ‘™π‘–π‘›π‘’ π‘šπ‘Žπ‘Ÿπ‘˜π‘’π‘

𝑋

π‘œ / + .2𝑋+𝑋 / 𝐷𝑕′ π‘„π‘œ π‘œ

In (30), the first three terms are similar to the optimal hub airport charge, consisting of airport operating cost, residual congestion delay cost and a rebate accounting for airlines’ market power. The rebate is equal to a weighted-average of the airline markups in both local markets and the connecting market. The last two terms reflecting the interaction between local passengers and connecting passengers in congestion delay cost, especially in the hub airport where the connecting passengers have to take two aircraft movements in order to complete their journey. 4.3. Airlines’ ticket price under public airports From airline first-order conditions (10) and (11), the airline ticket prices can be derived as follows: 1𝜌

(31)

𝑃 = (𝑑 + πœ‡π‘• + πœ‡π‘— ) + 𝑁1 (𝐷′ + 𝐷𝑕′ )(𝑄 + π‘„π‘œ ) + .𝑁 πœ€ /,

(32)

π‘ƒπ‘œ = 2 2(𝑑 + πœ‡π‘• + πœ‡π‘— ) + 𝑁1 (𝐷′ + 𝐷𝑕′ )(𝑄 + π‘„π‘œ ) + 2 .𝑁 πœ€ π‘œ /3.

1

1𝜌

π‘œ

These pricing rules indicate that the airlines’ ticket price will consist of airline operating 1

cost, airport charges from hub airport and local airport(s), a portion .𝑁/ of congestion delay cost to be internalized by the airline, and a markup reflecting airline market power. The airport charges are exogenous to the carriers, to be set by the airport authorities in 14

the first stage. Substituting (25) and (30) into airlines’ pricing rules (31) and (32), we respectively obtain the ticket prices that local passengers and connecting passengers will pay to a representative carrier: (33)

1

1

2𝑋

𝑃(πœ‡π‘•π‘π‘’π‘ , πœ‡ 𝑝𝑒𝑏 ) ≑ 𝑃𝑒𝑏 = (𝑑 + 𝑐𝑗 + 𝑐𝑕 ) + 0.2 βˆ’ 𝑁/ βˆ’ 𝑁 .2𝑋+𝑋 /1 (𝐷′ + ⏟ π‘œ π‘π‘œπ‘Ÿπ‘‘π‘–π‘œπ‘› π‘œπ‘“ π‘π‘œπ‘›π‘”π‘’π‘ π‘‘π‘–π‘œπ‘› π‘π‘œπ‘ π‘‘ 2𝑋

1𝜌

1 3𝜌

2𝑋

𝜌

𝑋

π‘œ 𝐷𝑕′ )(𝑄 + π‘„π‘œ ) + 0.2𝑋+𝑋 / 𝐷′ + 𝐷𝑕′ 1 π‘„π‘œ + .𝑁 πœ€ / βˆ’ 𝑁 02 πœ€ π‘œ .2𝑋+𝑋 / + 2 πœ€ .2𝑋+𝑋 /1, ⏟ π‘œ π‘œ π‘œ π‘œ

π‘Ÿπ‘’π‘π‘Žπ‘‘π‘’π‘  𝑏𝑦 𝑕𝑒𝑏 π‘Žπ‘›π‘‘ π‘™π‘œπ‘π‘Žπ‘™ π‘Žπ‘–π‘Ÿπ‘π‘œπ‘Ÿπ‘‘π‘ 

(34)

1

1

2𝑋

π‘ƒπ‘œ (πœ‡π‘•π‘π‘’π‘ , πœ‡ 𝑝𝑒𝑏 ) ≑ π‘ƒπ‘œπ‘’π‘ = 2 {(𝑑 + 𝑐𝑗 + 𝑐𝑕 ) + 0.2 βˆ’ 𝑁/ βˆ’ 𝑁 .2𝑋+𝑋 /1 (𝐷′ + ⏟ π‘œ π‘π‘œπ‘Ÿπ‘‘π‘–π‘œπ‘› π‘œπ‘“ π‘π‘œπ‘›π‘”π‘’π‘ π‘‘π‘–π‘œπ‘› π‘π‘œπ‘ π‘‘ 2𝑋

1 𝜌

1 3𝜌

2𝑋

𝜌

𝑋

π‘œ 𝐷𝑕′ )(𝑄 + π‘„π‘œ ) + 0.2𝑋+𝑋 / 𝐷′ + 𝐷𝑕′ 1 π‘„π‘œ + .2𝑁 πœ€ π‘œ / βˆ’ 𝑁 02 πœ€ π‘œ .2𝑋+𝑋 / + 2 πœ€ .2𝑋+𝑋 /1}, ⏟ π‘œ π‘œ π‘œ π‘œ π‘œ

π‘Ÿπ‘’π‘π‘Žπ‘‘π‘’π‘  𝑏𝑦 𝑕𝑒𝑏 π‘Žπ‘›π‘‘ π‘™π‘œπ‘π‘Žπ‘™ π‘Žπ‘–π‘Ÿπ‘π‘œπ‘Ÿπ‘‘π‘ 

where the superscript β€œπ‘’π‘β€ stands for the prices under public airports. From (25) and (30), we see that the hub airport, as well as a local airport, charges the 1

congestion delay cost (𝐷′ + 𝐷𝑕′ )(𝑄 + π‘„π‘œ ) with a portion of .1 βˆ’ 𝑁/. From (33), we know that local passengers will pay a portion of the congestion delay cost included in 1

π‘₯

2𝑋

the ticket price as 0.2 βˆ’ 𝑁/ βˆ’ 𝑁1, where π‘₯ ≑ .2𝑋+𝑋 / ∈ (0, 1). Given that π‘œ

(35)

1

π‘₯

1

π‘₯

βˆ†π‘π‘ 𝑒𝑏 ≑ 0.2 βˆ’ 𝑁/ βˆ’ 𝑁1 βˆ’ .1 βˆ’ 𝑁/ = .1 βˆ’ 𝑁/ > 0,

we see that local passengers will over-pay the congestion delay cost. A similar argument applies to connecting passengers.

15

Furthermore, the total rebates from the hub and local airports to a network carrier, which are the summation of airline markups in (25) and (30), results in a decrease in the ticket price (i.e., last term of (33)). This implies that local passengers (as well as connecting passengers) enjoy a rebate twice, once from the hub airport and the other from the local airports. These lead to the following proposition:

Proposition 1. In a hub-spoke network with congestion, while both the hub and local airports are maximizing social welfare, the passengers will eventually pay a ticket price that overcharges the congestion delay cost and overcompensates for airline markups.

Proposition 1 can be intuitively explained as follows. As each airport authority considers social welfare of its users, including airlines and passengers, while taking airport charge by the other airports as given, each airport will levy residual congestion charges to maximize social welfare, so that passengers will pay a ticket price equal to social marginal costs. In fact, each airport charge includes (𝐷′ + 𝐷𝑕′ )(𝑄 + π‘„π‘œ ), which already accounted for congestion costs at both airports. However, as each airport taking the other airport charge as exogenous, both airports will levy residual congestion charges. As a result, the passenger will eventually pay a ticket price which includes

16

double residual congestion charges. Similarly, the airport rebate for airline market power will also be doubled in the final ticket price. Proposition 1 leads to an interesting scenario, where all airports in the network are owned or coordinated by a central authority. In this scenario, airport charges will be centrally determined so as to induce social-marginal-cost pricing by the airlines. Brueckner (2005) has constructed this type of network model. On the other hand, Pels and Verhoef (2004) stressed that in reality, one may have two regulators, each regulating an airport and they first looked at this issue using a parametric model and concluded that uncoordinated welfare-maximization could lower welfare. 5. Airport charge for private airports 5.1 Profit-maximizing hub airport’s charge The formulation for a private hub airport pursuing profit maximization can be written as (36)

π‘šπ‘Žπ‘₯πœ‡β„Ž Π𝑕 = 2(πœ‡π‘• βˆ’ 𝑐𝑕 )(𝑄 + π‘„π‘œ ).

The first-order condition for its optimal charge is: (37)

πœ•π‘„

(𝑄 + π‘„π‘œ ) + (πœ‡π‘• βˆ’ 𝑐𝑕 ) .

πœ•πœ‡β„Ž

πœ•π‘„

+ πœ•πœ‡π‘œ / = 0. β„Ž

Solving the above equation, we obtain: (38) Let βˆ’ .

πœ•π‘„

πœ•π‘„

πœ‡π‘• = 𝑐𝑕 βˆ’ (𝑄 + π‘„π‘œ )⁄.πœ•πœ‡ + πœ•πœ‡π‘œ /. β„Ž

β„Ž

πœ•(𝑄+π‘„π‘œ ) πœ•πœ‡β„Ž

⁄(𝑄 + π‘„π‘œ )/ πœ‡π‘• ≑ πœ€π‘• , equation (38) can be rewritten as

17

πœ‡

πœ‡π‘• = 𝑐𝑕 + πœ€ β„Ž .

(39)

β„Ž

This is a standard result that a profit-maximizing airport will levy an airport charge which equals airport operating cost plus a markup reflecting market power of the airport. By similar method, we can also derive the optimal airport charge for a private local airport 𝑗, pursuing profit maximization, as follows. πœ‡

πœ‡π‘— = 𝑐𝑗 + πœ€ 𝑗.

(40)

𝑗

Comparing (39) with (25) and (40) with (30), respectively, we see that the airport charges of the private airports do not depend on 𝑁, while that of welfare-maximization airports will increase in 𝑁 , with 𝑁 = 1 leading to negative charge: no marginal-congestion-delay cost but full rebates on airline markups. 5.2 Airlines’ ticket price under private airports First, substituting (15)-(16) into (38) yields the charge of a private hub airport: 1

1

1

𝑋𝑋

πœ‡π‘•π‘π‘Ÿπ‘– = 𝑐𝑕 + 2 .1 + 𝑁/ (𝑄 + π‘„π‘œ )(𝐷′ + 𝐷𝑕′ ) βˆ’ 2𝑁 (2𝑋+π‘‹π‘œ ) (𝑄 + π‘„π‘œ ) +

(41)

π‘œ

1 2𝑁

(𝑄 + π‘„π‘œ )2 (𝐷 β€²β€² + 𝐷𝑕′′ ).

Similarly, the airport charge of a private local airport is (42)

1

1

𝑋𝑋

1

π‘œ (𝑄 + π‘„π‘œ ) + (𝑄 + πœ‡ π‘π‘Ÿπ‘– = 𝑐𝑗 + .1 + 𝑁/ (𝑄 + π‘„π‘œ )(𝐷′ + 𝐷𝑕′ ) βˆ’ 𝑁 (2𝑋+𝑋 ) 𝑁 π‘œ

π‘„π‘œ )2 (𝐷′′ + 𝐷𝑕′′ ).

18

Next, substituting the corresponding pairs from (25), (30), (41) and (42) into airlines’ pricing rules (31) and (32), we obtain the ticket prices paid by local passengers and connecting passengers under the cases of two mixed public/private airports and that of all private airports. Because the arguments for connecting passengers are similar, we can focus on the local passengers only. Case rj (privatized airport j): A public hub airport and a private local airport 1

𝑃(πœ‡π‘•π‘π‘’π‘ , πœ‡ π‘π‘Ÿπ‘– ) ≑ π‘ƒπ‘Ÿπ‘— = (𝑑 + 𝑐𝑗 + 𝑐𝑕 ) + .2 + 𝑁/ (𝐷′ + 𝐷𝑕′ )(𝑄 + π‘„π‘œ ) +

(43) 1 𝑁

(𝑄 + π‘„π‘œ )2 (𝐷′′ + 𝐷𝑕′′ ) +

1𝜌

1

𝜌

2𝑋

𝜌

𝑋

1

𝑋𝑋

π‘œ π‘œ (𝑄 + π‘„π‘œ ). βˆ’ 𝑁 02πœ€π‘œ .2𝑋+𝑋 / + πœ€ .2𝑋+𝑋 /1 βˆ’ 𝑁 (2𝑋+𝑋 π‘πœ€ ⏟ π‘œ π‘œ π‘œ π‘œ)

π‘Ÿπ‘’π‘π‘Žπ‘‘π‘’ π‘‘π‘’π‘Ÿπ‘šπ‘ 

Case rh (privatized hub airport): A private hub airport and a public local airport 3

1

π‘₯

𝑃(πœ‡π‘•π‘π‘Ÿπ‘– , πœ‡ 𝑝𝑒𝑏 ) ≑ π‘ƒπ‘Ÿπ‘• = (𝑑 + 𝑐𝑗 + 𝑐𝑕 ) + 0.2 + 2𝑁/ βˆ’ 𝑁1 (𝐷′ + 𝐷𝑕′ )(𝑄 + π‘„π‘œ ) +

(44)

2𝑋

1𝜌

1 𝜌

2𝑋

𝜌

𝑋

1

𝑋𝑋

π‘œ π‘œ (𝑄 + π‘„π‘œ ) + 0.2𝑋+𝑋 / 𝐷′ + 𝐷𝑕′ 1 π‘„π‘œ + 𝑁 πœ€ βˆ’ 𝑁 0 πœ€ π‘œ .2𝑋+𝑋 / + πœ€ .2𝑋+𝑋 /1 βˆ’ 2𝑁 (2𝑋+𝑋 ⏟ π‘œ π‘œ π‘œ π‘œ π‘œ)

π‘Ÿπ‘’π‘π‘Žπ‘‘π‘’ π‘‘π‘’π‘Ÿπ‘šπ‘  1 2𝑁

(𝑄 + π‘„π‘œ )2 (𝐷 β€²β€² + 𝐷𝑕′′ ).

Case ri: All airports are private 3

5

𝑃(πœ‡π‘•π‘π‘Ÿπ‘– , πœ‡ π‘π‘Ÿπ‘– ) ≑ π‘ƒπ‘Ÿπ‘– = (𝑑 + 𝑐𝑗 + 𝑐𝑕 ) + .2 + 2𝑁/ (𝑄 + π‘„π‘œ )(𝐷 β€² + 𝐷𝑕′ ) +

(45) 3 2𝑁

1𝜌

(𝑄 + π‘„π‘œ )2 (𝐷 β€²β€² + 𝐷𝑕′′ ) + .

π‘πœ€

3

𝑋𝑋

π‘œ (𝑄 + π‘„π‘œ ). / βˆ’ 2𝑁 (2𝑋+𝑋 ) π‘œ

The following comparisons show the degree of overcharge of congestion delay cost to 1

local passengers, as compared with the benchmark portion .1 βˆ’ 𝑁/. (46)

1

1

2

βˆ†π‘π‘ π‘Ÿπ‘— ≑ .2 + 𝑁/ βˆ’ .1 βˆ’ 𝑁/ = .1 + 𝑁/ > 0, 19

3

1

π‘₯

1

1

3

π‘₯

(47)

βˆ†π‘π‘ π‘Ÿπ‘• ≑ 0.2 + 2𝑁/ βˆ’ 𝑁1 βˆ’ .1 βˆ’ 𝑁/ = .2 + 2𝑁 βˆ’ 𝑁/ > 0,

(48)

βˆ†π‘π‘ π‘Ÿπ‘– ≑ .2 + 2𝑁/ βˆ’ .1 βˆ’ 𝑁/ = .2 + 2𝑁/ > 0.

3

5

1

1

7

From (46)-(48), we see that network carriers overcharge congestion delay costs on passengers in each case. Moreover, including (35) into the following comparisons, we have 2+π‘₯

(49)

βˆ†π‘π‘ π‘Ÿπ‘— βˆ’ βˆ†π‘π‘ 𝑒𝑏 =

(50)

βˆ†π‘π‘ π‘Ÿπ‘• βˆ’ βˆ†π‘π‘ π‘Ÿπ‘— = βˆ’ .2 + 2𝑁 + 𝑁/ < 0

(51)

βˆ†π‘π‘ π‘Ÿπ‘• βˆ’ βˆ†π‘π‘ π‘Ÿπ‘– = βˆ’ .

𝑁

> 0,

1

2+π‘₯ 𝑁

1

π‘₯

/ < 0.

Proposition 2. In a hub-spoke network, the degree of overcharge of congestion delay costs on passengers a) under a public hub airport combined with private local airports is greater than that under all public airports. b) under a private hub airport combined with public local airports is smaller than that under a public hub and private local airports combination; it is also smaller than that under all private airports.

Proposition 2 has policy implications on airport privatization schemes. The results

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show that privatizing local airports will always lead to higher degree of overcharge for congestion delay costs, whether the hub is a public or privatized airport. Therefore, in airport privatization schemes, increasing distortions in congestion charges would be a consideration against local airport privatization. In this consideration, privatizing the hub airport would be preferred to privatizing local airports. Furthermore, comparing degrees of overcharge under different ownership schemes gives: 1

3

(52)

βˆ†π‘π‘ π‘Ÿπ‘• βˆ’ βˆ†π‘π‘ 𝑒𝑏 = .βˆ’ 2 + 2𝑁/ β‹š 0 ↔ 𝑁 β‹› 3,

(53)

βˆ†π‘π‘ π‘Ÿπ‘– βˆ’ βˆ†π‘π‘ π‘Ÿπ‘— = .βˆ’ +

(54)

βˆ†π‘π‘ π‘Ÿπ‘– βˆ’ βˆ†π‘π‘ 𝑒𝑏 = .βˆ’ 2 + 2𝑁 + 2𝑁/ β‹š 0 ↔ 𝑁 β‹› (7 + 2π‘₯),

1

3

2

2𝑁

1

7

/ β‹š 0 ↔ 𝑁 β‹› 3, 2π‘₯

Proposition 3. The degree of overcharge of congestion delay costs on passengers a) under a private hub and public local airports is smaller than that under all public airports if the number of network carriers is more than three. b) under all private airports is smaller than that under a pubic hub and private local airports as long as the number of network carriers is more than three. c) under all private airports is smaller than that under all public airports if the airline network markets are competitive.

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The results in Proposition 3 indicate that airline market structure also has important implications on airport privatization policy. Specifically, if airline market structure is more competitive, privatizing the hub airport would lead to less distortion in congestion charges, whether the local airports are public or privatized. Combining the results of both Proposition 2 and Proposition 3, we would conclude that, under competitive airline market structure, it would be preferable to privatize a hub airport than to privatize local airports. Finally, let us highlight on the rebate terms concerning airline markups including both local and connecting markets. By respectively comparing the corresponding term in (33), 𝜌

2𝑋

𝜌

𝑋

π‘œ (43), (44) and (45) from the benchmark value, 0 πœ€ π‘œ .2𝑋+𝑋 / + πœ€ .2𝑋+𝑋 /1, we have: π‘œ

π‘œ

π‘œ

Proposition 4. a) There are no rebates in airport charges for airline markups under all privatized airports network. However, there are rebates in a network involving at least one public airport and the degree of rebates is largest under all public airports. b) In the network with a pubic hub and private local airports (with all public airports), the rebate undercompensates (overcompensates) for airline markups. However, the

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degree of rebates under a private hub and public local airports just compensates for airline markups.

It is interesting to see that the results of Proposition 4 have similar policy implications on airport privatization scheme, as in Propositions 2 and 3. Specifically, considerations on compensating for airline markups also suggest that it would be preferable to privatize a hub airport than to privatize local airports. 6. Concluding remarks This study used a simple hub-spoke network that links three cities, to investigate network carriers’ pricing and airport congestion charges with various combination of public/private ownership. The analytical results of the present study contribute the interesting points to the literature. In essence, from the perspective of economic efficiency concerning congestion delay costs and airline markups, privatizing only the hub airport in a hub-spoke network could be socially desirable, whereas privatizing local airports only may worsen welfare. These results have policy implications to the airport privatization scheme and are generally in favor of privatizing a hub airport. In the real world, we can observe that a number of governments privatizing their major (hub) airports (e.g., Heathrow, Gatwick, Copenhagen Kastrup, Zurich, Sydney

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Kingsford Smith, Auckland) rather than local airports. Ignoring some other complications, our Propositions 2 to 4 may provide a justification for privatization of major hub airports from the viewpoint of economic efficiency. Our finding that airline market structure has important implications on airport privatization policy (proposition 3) also suggests that an empirical study that examines the relationship between airline market structure and ownership of hub and local airports could be a promising future work. Finally, we suggest some other directions for future research. First, in the previous network model by Pels and Verhoef (2004), Flores-Fillol (2010) and in the present model, the single hub airport and local airports are complementary agents (without competition between the airports). Also, in Brueckner (2005)’s network, multiple hub airports are considered but all are owned and operated by one single public authority. Therefore, extending the existing network to include hub-airport competition under separate authorities should be an interesting future work. Second, formulating a more realistic model to allow the load factor to be endogenous and/or extending to a long-run analysis in which carriers can choose aircraft size also remains as valuable future research.

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References Brueckner, J.K. 2002. Airport congestion when carriers have market power. American Economic Review, 92, 1357-1375. Brueckner, J.K. 2005. Internalization of airport congestion: A network analysis. International Journal of Industrial Organization, 23, 599-614. Brueckner, J.K., Verhoef, E.T. 2010. Manipulable congestion tolls. Journal of Urban Economics, 67, 315-321. Flores-Fillol, R. 2010. Congested hubs. Transportation Research Part B, 44, 358-370. Pels, E. and Verhoef, E.T. 2004. The economics of airport congestion pricing. Journal of Urban Economics, 55, 257-277. Oum, T.H., Adler, N., Yu, C. 2006. Privatization, corporatization, ownership forms and their effects on the performance of the world’s major airports. Journal of Air Transport Management 12, 109-121. Oum, T.H., Yan, J., Yu, C. 2008. Ownership forms matter for airport efficiency: A stochastic frontier investigation of worldwide airports. Journal of Urban Economics 64, 422-435. Zhang, A. and Zhang, Y. (2006), Airport capacity and congestion when carriers have market power. Journal of Urban Economics, 60, 229-247.

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