Airline Route Structure Competition and Network Policy

Transcription

1 TI /VIII Tnbergen Insttute Dscusson Paper Arlne Route Structure Competton and Network Polcy Hugo Emlo Slva Erk Verhoef Vncent van den Berg Faculty of Economcs and Busness Admnstraton, VU Unversty Amsterdam, and Tnbergen Insttute, The Netherlands.

2 Tnbergen Insttute s the graduate school and research nsttute n economcs of Erasmus Unversty Rotterdam, the Unversty of Amsterdam and VU Unversty Amsterdam. More TI dscusson papers can be downloaded at Tnbergen Insttute has two locatons: Tnbergen Insttute Amsterdam Gustav Mahlerplen MS Amsterdam The Netherlands Tel.: +31(0) Tnbergen Insttute Rotterdam Burg. Oudlaan PA Rotterdam The Netherlands Tel.: +31(0) Fax: +31(0) Dusenberg school of fnance s a collaboraton of the Dutch fnancal sector and unverstes, wth the ambton to support nnovatve research and offer top qualty academc educaton n core areas of fnance. DSF research papers can be downloaded at: Dusenberg school of fnance Gustav Mahlerplen MS Amsterdam The Netherlands Tel.: +31(0)

3 Arlne route structure competton and network polcy Hugo E. Slva, Erk T. Verhoef, Vncent A.C. van den Berg Department of Spatal Economcs, VU Unversty Amsterdam, De Boelelaan 1105, 1081 HV Amsterdam, The Netherlands. Tnbergen Insttute, Gustav Mahlerplen 117, 1082 MS, Amsterdam, The Netherlands. Abstract Ths paper studes whether a regulator needs to correct the route structure choce by carrers wth market power n the presence of congeston externaltes, n addton to correct ther prcng. We account for passenger benefts from ncreased frequency, passenger connectng costs, arlne endogenous hub locaton and route structure strategc competton. We fnd that, for some parameters, an nstrument drectly amed at regulatng route structure choce may be needed to maxmze welfare, n addton to per-passenger and per-flght tolls desgned to correct output neffcences. Ths holds true when the regulator s constraned to set non-negatve tolls, but also for the case of unconstraned tollng. Keywords: Route structure competton, Avaton polcy, Hub-and-spoke networks, Fully-connected networks 1. Introducton Followng the deregulaton of the arlne ndustry, several changes n avaton markets were observed (see Morrson and Wnston (1995) for an overvew of the changes n the US ndustry, and Burghouwt and Hakfoort (2001) for Europe). In addton to changes n fares, the most notorous change was n the way markets were served: the adopton of hub-andspoke route structures by carrers became domnant. Such a decson by carrers has often been explaned wth three arguments: economes of densty, frequency effects and strategc advantages. The frst refers to the fact that average cost n a drect route decreases wth the number of passengers, and the second to the fact that there are benefts for passengers of ncreased frequences, e.g. reductons n schedule delay costs (the dfference between desred and actual departure/arrval tme). Both may be better exploted under hub-andspoke structures. In a monopoly framework, Hendrcks et al. (1995) show that economes of densty alone can nduce an arlne to adopt a hub-and-spoke route structure; Pels et al. (2000) analyze the choce of route structure under lnear margnal costs and the effect Correspondng author Emal addresses: h.slvamontalva@vu.nl (Hugo E. Slva), e.t.verhoef@vu.nl (Erk T. Verhoef), vberg@feweb.vu.nl (Vncent A.C. van den Berg)

4 of fxed costs n the decson; and Brueckner (2004) shows how frequency effects favors the adopton of hub-and-spoke. The thrd argument, strategc advantages, refers to the fact that adoptng hub-and-spoke route structures may brng, n olgopolstc competton, further advantages because of the effect t may have on compettors. For nstance, Oum et al. (1995) show that usng a hub-and-spoke structure can be a top-dog strategy, n the sense of Fudenberg and Trole (1984), allowng the carrer to be more aggressve n output market competton; t can deter entry n hub markets f the complementartes among hub markets are large, or the number of complementary hub markets s large (Hendrcks et al., 1997); and t can prevent competton n local markets between two hub carrers because nvadng the compettor s local market may reduce own proft n all connectng markets due to a more aggressve competton n the trans-hub market (Zhang, 1996). The outcomes of a deregulated envronment where carrers can choose how to serve markets, and the condtons that gve rse to hub-and-spoke route structures as an equlbrum of unregulated competton, have been well studed n the lterature. Recent contrbutons nclude Hendrcks et al. (1999), Aldergh et al. (2005), Barla and Constantatos (2005), and Flores-Fllol (2009, 2010). These studes, however, gnore the endogenous nature of the hub locaton, do not study the socally optmal route structure, and most of them also gnore congeston effects. On the other hand, lterature on prcng and regulaton n avaton markets has mostly focused on ether a sngle orgn destnaton par, hence gnorng network effects, or n networks wth fxed route structures, hence gnorng ts endogenous nature and ts effect on optmal polcy. The objectve of ths paper s to extend the congeston prcng and regulaton analyss by elaboratng on polcy nstruments that can decentralze the socally effcent outcome n a network settng, where carrers wth market power choose a route structure n the presence of congeston externaltes. It s known from earler lterature, whch abstracts away from endogenous route structure, that olgopolstc carrers partally nternalze congeston and exert market power (e.g. Brueckner (2002); Pels and Verhoef (2004)). Ths means that two neffcences need to be corrected: the dead-weght loss from market-power markups (e.g. wth subsdes) and the excessve number of flghts that are scheduled (e.g. wth slot constrants or congeston prcng). 1 In ths paper, we study whether and how the ncluson of route structure choce by carrers changes these conclusons. Specfcally, do regulators need an addtonal nstrument, on top of the ones descrbed above, to nduce the socally desrable outcome? We carry out the analyss n what we beleve s the smplest possble settng that allows us to account for strategc nteractons n route structure choce, endogenous hub locatons, market power exerton by arlnes, congeston externaltes at arports, and passenger frequency benefts and transfer costs. 1 See Zhang and Czerny (2012) for an up-to-date revew on arport prcng. 2

5 The man result of our analyss s that a regulatory nstrument drectly targeted on route structure choce may be needed to maxmze welfare, n addton to tolls desgned to nduce the effcent outputs, gven the networks chosen. We fnd that socal welfare can be ncreased by usng an addtonal polcy nstrument when the regulator s restraned from subsdzng arlnes, but also when t does not face such constrant on tollng. Specfcally, the frst-best optmal route structures and output levels cannot always be decentralzed by just usng an arlne- and market-specfc per-passenger toll (to correct for market power), together wth an arlne- and lnk-specfc per-flght toll (to correct for congeston), desgned to nduce the effcent output for the optmal route structure. Thus, the equlbrum wth those tolls s not always effcent, even when the regulator can perfectly dscrmnate arlnes and has no prcng constrants. Ths s because these tolls, especally the market-specfc per-passenger subsdes, whch are requred to counteract market power exerton, provde ncentves to arlnes to adopt the route structure that better explots the subsdes, and whch may dffer from the one that maxmzes welfare. Frst-best prcng as just dscussed typcally requres a regulator to gve asymmetrc per-passenger subsdes to arlnes, a polcy that s arguably, n practce, mpossble to mplement. To address ths lmtaton, we also study the case n whch the regulator s constraned to charge non-negatve tolls. We show that when the second-best optmal route structure s dfferent to the outcome of unregulated competton, second-best tolls may not nduce the second-best optmal equlbrum. That s, the route structure and output levels that maxmze welfare n absence of market power correctons possbly cannot be decentralzed through tolls alone. Thus, also n the absence of subsdzaton, tolls desgned to correct output neffcences are not always a suffcent nstrument for (constraned) welfare maxmzaton. Our results may have mportant polcy mplcatons. In some cases an nstrument drectly amed at regulatng route structure choce s needed for welfare maxmzaton, and n the cases where the prcng nstruments are suffcent, the ratonale for the charges s not always the same. In some cases they are requred only to correct output choces, n other cases the tolls are needed to correct smultaneously output and route structure choces, and fnally they can also be needed n order to change the market structure n terms of supplers present n the network, n addton to correct output and route structure. It s therefore evdent from the analyss that a regulator desgnng a prcng polcy for the avaton ndustry has to take nto account ts effect on the long-run route structure equlbrum, and assess the optmalty of the observed settng before decdng on toll levels. In addton, more nformaton s needed to acheve the frst-best: f only local varables (notably margnal external cost and margnal beneft) are avalable, adaptve prcng would gude the regulator to the (second-best) optmum. But, wth dscrete changes n route structures, and multple local optma, ths s no longer true. A nave regulator, who 3

6 observes a sub-optmal route structure confguraton, and set the tolls based on ths, may not always acheve welfare maxmzaton, nether frst-best nor second-best. Fnally, the extent to whch each of the dfferent stuatons descrbed above hold s a matter of emprcal research. In Secton 2 we ntroduce the model and the confguraton of nodes between whch endogenous route structures can be offered. Secton 3 analyzes the equlbra of the untolled competton for a duopoly, whle Secton 4 derves the welfare maxmzng equlbra. Secton 5 studes whether prcng s enough to acheve the welfare maxmzng settng as the result of tolled competton, and extends the analyss to the second-best case where the regulator cannot subsdze arlnes. Fnally, Secton 6 concludes. 2. The model In order to keep the smplest possble focus on the route structure choce by agents wth market power n presence of externaltes, we use a stylzed model that follows Brueckner s (2004) n the basc assumptons, and extends t by consderng congeston, arlne competton and the analyss of how to enforce the socal optmum. We consder a symmetrc duopoly of arlnes that compete n each of the three symmetrc markets that are shown n Fgure 1. These markets M = {AB, BC, AC} represent returntrps for smplcty (e.g. people travel from A to B and return); drecton-specfc returntrps (e.g. people makng round-trps both from A to B and from B to A) may be ntroduced wthout alterng the analyss. The lnks L = {ab, bc, ac} are always avalable to any arlne; that s, both arlnes have permsson to schedule flghts between any cty-par. Each market m can be served by arlnes ether drectly, flyng non-stop from the orgn arport to the destnaton arport, or va a hub arport that an arlne chooses to use for the connecton. As a result, the two possble route structures for an arlne are: fully connected (henceforth F); or hub-and-spoke (henceforth H), where they choose one arport as ts hub, and fly only between the hub and the two remanng arports, servng two markets non-stop and one wth connectng flghts. 2 We let each arlne s hub to be endogenous, therefore asymmetrc settngs wth hub-and-spoke structures may arse. We model the arlnes competton wth a two-stage game where, frst, carrers smultaneously choose route structure, and then they compete n output at a market level. Specfcally, n the latter stage, arlnes have the number of passengers n each market (q m ), number of flghts n each lnk (f l ), and arcraft sze (s l ) as strategc varables; ths s an extenson of the Cournot assumpton that arlnes take rval s quanttes, nstead of fares, 2 Equlbra where an arlne chooses to serve less than the 3 orgn-destnaton pars wll be consdered n the numercal model. 4

7 B ab bc A ac Fgure 1: Network C as gven. 3 We assume that the full prce faced by a passenger when travelng wth arlne, s: θ m = p m + D m + g m. (1) Ths s the sum of the fare, p m, the congeston delay cost, Dm, and schedule delay cost, g m.4 We further assume that arlnes are perceved as mperfect substtutes and that the passenger demand functon for an arlne n market m, q m, s lnear n own and the rval s prce. Therefore, the demand faced by the arlne depends on ts own full prce, θ m, as well as ts rval s, θj m (hereafter, when subscrpt j appears n the same expresson wth, t refers to the rval arlne). These assumptons are summarzed n the followng nverse demand: θ m = A B q m E qj m, (2) where A, B, and E are postve parameters satsfyng 0 E B. Note that we gnore demand dependences between markets (cty-pars). Ths set of assumptons allows us to analyze the effect of arlne horzontal dfferentaton on route structure choce by means of varyng the rato of substtutablty, E/B, that ranges from 0 when the arlnes outputs are ndependent n terms of demand nteracton to 1 when the arlnes outputs are perfect substtutes. At the same tme, we consder that not all passengers choose the arlne wth the most attractve fare-delay combnaton due to factors that may dffer across carrers, such as servce level (e.g. language), and make passengers perceve arlnes as mperfect substtutes. 3 The assumpton that arlnes compete n a Cournot fashon s common n the arlne lterature and s supported by emprcal evdence by Brander and Zhang (1990) and Oum et al. (1993). For a dscusson of the mplcatons of leadershp behavor see Brueckner and Van Dender (2008), and for Bertrand competton wth dfferentated arlnes see Slva and Verhoef (2013). 4 The schedule delay s the tme dfference between a passengers desred departure tme and the actual departure tme. As we do not explctly model trp-tmng decsons, ths represents an average measure of the schedule delay cost, that, at least, provdes the rght ntuton. 5

8 Followng Brueckner (2004), we model the arlnes cost per flght as a functon of the arcraft sze (s) n the followng way: C(s) = c f + c q s, (3) where c f s the fxed cost per flght, and c s the margnal cost per seat. Ths formulaton captures n a smple way that ncreasng the number of passengers per lnk may reduce average cost per passenger through economes of seats. We also assume a constant load factor of 100% that allows for analytcal tractablty. A more realstc model would have endogenous arcraft sze and load factors, wth stochastc demand, but ths would prevent us from provdng analytcal transparent understandng of route structure equlbra. As a natural benchmark, we consder a regulator that controls all arports and maxmzes welfare, so that we analyze a three-stage game. In the frst stage, the regulator sets perpassenger tolls to each arlne n each market (τ m ), and per-flght tolls to each arlne n each lnk (τ l).5 In the second and thrd stage, arlnes choose route structure and output respectvely. 6 We look at sub-game perfect equlbra through backward nducton, so we frst analyze, n the followng secton, the arlnes Nash equlbra. 3. Arlnes equlbrum In the second stage, arlnes have a dscrete choce between alternatve route structures (F or H at any of the arports). Hence, we frst look at ther profts whle takng route structures as gven, and then analyze the equlbrum n route structure The fully connected route structure In ths settng, arlne uses F as ts route structure, and chooses the frequency on each lnk, f l; and the number of passengers n each market, qm. The seats per flght are s l = ql /f l, where ql s the number of passengers flyng through lnk l, because there s no gan of havng spare capacty. We assume that the average schedule delay depends only on the flght frequency of the arlne n the lnk that connects that market, and that t decreases wth frequency (e.g. g AB / f ab < 0 g AB / f l = 0 l ab gab / fj l = 0 l). The assumpton that schedule delay does not depend on the rval s frequency, as congeston does, reflects our vew that, n the dfferentated duopoly, frequency s perceved as an arlne-specfc attrbute. 5 Ths formulaton s a reduced form of a system of welfare maxmzng arports, or a regulator, settng charges per passenger and charges per flght at each arport. The dfference would matter f each arport s controlled by a dfferent authorty, that may, for nstance, maxmze local welfare. 6 We assume that arlnes treat the tolls as parametrc,.e. they do not beleve that ther actons may change the way a regulator chooses nstruments. See Brueckner and Verhoef (2010) for a detaled dscusson on how to account for such behavor of agents wth market power n presence of externaltes. 6

9 We also assume that there s congeston at the orgn and destnaton, that arport runway congeston depends on total number of flghts at that arport, and that t ncreases n the total number of flghts. For example, denotng F l = f l + f j l the total number of flghts on lnk l, the full prce faced by a passenger of market AB flyng wth arlne s: θ AB = p AB + D(F ab + F ac, K A ) + D(F ab + F bc, K B ) + g AB (f ab ), (4) where D s the delay cost functon, assumed common to all arports. The full prce then equals the sum of the fare; the congeston at the orgn, A, whch depends on the total number of flghts operatng at that arport (F ab + F ac ) and the arport s capacty (K A ); the congeston at the destnaton arport, B; and the schedule delay cost. 7 We look at the partcular case where all arports have the same capacty, but ths could easly be extended. The arlne s proft, usng (3) and s l = ql /f l, s: π F = m M q m (p m c q τ m ) l L f l (c f + τ l ), (5) where the superscrpt F refers to the fully connected structure. Usng ths, together wth (2), we can rewrte proft as: π F = m M q m (A B q m E q m j g m D m c q τ m ) l L f l (c f + τ l ). (6) Arlne proft ndrectly depends also on the rval s route structure. That structure wll be reflected n the rval s number of passengers and n number of flghts, whch wll affect demands and delays. What we do, n ths secton, s to look at the arlnes best response n output rrespectve of whch route structure underles the rval s quanttes, and then, when dervng the equlbrum n route structure, compare the dfferences that arse from the dfferent rval s route structure choces. The frst-order condtons for q m and f l mply the followng prcng and frequency settng rules: π F f l π F q m = 0 m M = 0 p m = c q + τ m + B q m, (7) q m ( D m f l + gm f l ) = c f + τ l. (8) Equaton (7) states that the fare charged by the arlne n market m s the sum of the margnal cost per capacty unt (c q ), the arport charge per passenger n that market (τ m ), and a conventonal markup reflectng carrer market power (B q m ). Equaton (8) states that arlne s margnal cost per flght (rght-hand sde of (8)) equals margnal revenue (left-hand sde, margnal congeston costs plus margnal schedule delay benefts). 7 Wthout loss of generalty, both delay functons, D and g, nclude the passengers valuaton of tme. 7

10 Therefore, arlnes nternalze own-passenger congeston. These rules are analogous to the rules obtaned prevously n Cournot competton (e.g. Pels and Verhoef, 2004). The arlne s proft usng a fully connected route structure, n sub-game equlbrum, s: Π F = m M B (q m ) 2 l L f l (c f + τ l ), (9) whch s obtaned by replacng Eq. (7) nto Eq. (6). Ths s the revenues from the markup (B q m per passenger) mnus the costs that are not drectly charged to passengers The hub and spoke route structure We now look at the case where an arlne () chooses to serve the markets wth a hub-and-spoke route structure. For llustraton purpose, we analyze n ths secton the case where the arlne chooses arport B as ts hub. Other cases are smply obtaned by changng notaton only. When we study the full game equlbrum, then t s necessary to explctly model the choce of hub arport. The changes wth respect to the fully connected case s that the market AC (the spoke market) s served wth connectng flghts at the hub. We assume, as n prevous studes of hub-and-spoke route structures, that the fare for the spoke market s set ndependently; ths mples that the fare for market AC s not restrcted to be equal to the sum of the fares of the two hub markets (AB and BC). The fares must, however, satsfy the arbtrage condton: the sum of the fares of the hub markets (n ths case, AB and BC) cannot be lower that the fare charged to the connectng passengers (market AC). The number of seats per flght, on each lnk, changes n ths case because, n addton to the passenger from hub markets, the passengers from the spoke market are also travelng through lnks ab and bc. As a consequence, n ths settng, arcraft szes wll satsfy: s ab s bc = (q AB = (q BC + q AC )/f ab, + q AC )/f bc. (10) Full prces n the hub markets have the same structure as before (see (4)), but they change n the spoke market. We assume that the passengers congeston delay s the sum of the delays at each leg, and that schedule delay cost for a hubbng passenger s the sum of the schedule delays of a passenger flyng both legs. Ths gves: D AC g AC = D AB = g AB + D BC, (11) + g BC. The defnton of g AC reflects our assumpton that g captures the schedule delay cost (frst term, g AB ), and that s also able to capture the transfer costs at the hub (second term, g BC ). Ths s a smple way to model the fact that leavng congeston and travel delays 8

11 asde a passenger ncurs an addtonal cost from connectng and that the cost s lower when the frequency of connectons s hgher. Although there s no reason why the transfer cost should be exactly equal to the schedule delay cost ncurred by a passenger travelng only the second leg, t s a convenent assumpton as for unequal frequences t s hard to express the frequency at the orgn-destnaton level. 8 the followng way: q AC π H = (A B q AC m {AB,BC} E q AC j These assumptons shape proft n q m (A B q m E q m j g m D m c q τ m ) + g AC D AC 2 c q T AC ) l {ab,bc} f l (c f + τ l ), (12) where the superscrpt H refers to the proft when an arlne s servng the markets wth a hub-and-spoke route structure. The dfference, besdes the new defnton of delays, s that, everythng else constant, an addtonal passenger n the AC market requres an ncrease of arcraft sze n both lnks, hence the cost per passenger s 2 c q. The frst-order condtons lead to the followng prcng and frequency settng rules: π H q m = 0 p m = c q + τ m + B q m m {AB, BC}, (13) π H f l = 0 π H q AC m {AB,BC} = 0 p AC (q m + q AC = 2 c q + T AC ( D m ) f l + gm f l + B q AC, (14) ) = c f + τ l l {ab, bc}. (15) These equatons state that arlnes apply a market power markup n each market and set frequency to equalze own margnal revenue wth own margnal cost, hence partally nternalzng congeston. In ths settng, the sub-game equlbrum proft, usng the frstorder condtons (Eqs. (13) and (14) n Eq. (12)), can be wrtten as: Π H = m M B (q m ) 2 l {ab,bc} f l (c f + τ l ). (16) Just as n the prevous case, t s the revenues from the markup mnus frequency costs that are not charged to passengers Second-stage: the choce of route structure In contrast to the thrd-stage, n ths stage the arlnes decson varables are dscrete. Arlnes ether serve the markets wth a fully connected route structure or wth a huband-spoke route structure. As we gnore the possblty of servng only one market n the 8 An alternatve assumpton used n the lterature s that passengers ncur a fxed cost when transferrng. The results do not change sgnfcantly f we assume ths nstead. 9

12 analytcal model, no other confguratons are possble. When an arlne chooses to use a hub-and-spoke structure, t also chooses whch arport to use as the hub. To characterze the equlbra, we need to compare the arlnes best responses, knowng the outcome of the thrd stage (quantty and frequency), for all the rval s possble route structures. Denote the route structure choce of an arlne as a choce of r RS = {F, H A, H B, H C }, where H x refers to a hub-and-spoke structure wth arport X as the hub. The relevant comparsons are the profts gven the route structure of the rval. Let Π (r, v) be the arlne s proft, evaluated at the outputs of the thrd-stage equlbrum, when t has chosen r as ts route structure, and the rval uses v. Then, t s straghtforward that a symmetrc settng wth both arlnes usng route structure r wll be an equlbrum of the arlnes game f and only f: Π (r, r) Π (u, r) u RS. (17) Because arlnes are symmetrc, whenever ths holds true for one arlne, t wll hold true for the other as well, and both arlnes havng r wll be a perfect sub-game equlbrum of the arlnes competton. Also note that, whenever both arlnes choose H A n equlbrum, both havng H B and both havng H C are also equlbra, because markets are symmetrc as well. We wll refer to ths set of equlbra as (H, H): both arlnes usng hub-and-spoke route structures and both usng the same arport as ther hub. It follows that (F, F ) s the equlbrum where both arlnes choose the fully connected route structure. As hub locaton s endogenous, asymmetrc equlbra where arlnes use dfferent hubs may arse. We denote ths set of possble equlbra as (H x, H y ), regardless of the locaton of the arlnes hubs. Asymmetrc equlbra, wth one arlne choosng route structure u and the other v ( u), wll arse f and only f the followng holds: Π (u, v) Π (w, v) Π (v, u) Π (y, u) w RS, y RS u v. (18) Ths mples that u s the best response when the rval chooses v and vce versa, whch agan, because of arlne and market symmetry, mples that there are multple equlbra for a partcular u and v. We denote (F, H) to the asymmetrc equlbra where one arlne serves the markets wth a fully connected route structure and the other wth a hub-andspoke route structure, regardless of the hub arport choce. Note that the above condtons, (17) and (18), are not necessarly mutually exclusve, therefore multple equlbra may arse. For nstance, t may be the case that for a certan parameter constellaton (F, F ) and (H x, H y ) are both equlbra. Despte havng a hghly stylzed model, these comparsons are hard to perform analytcally. To surpass ths, we look at some of the relevant equlbrum condtons that, together wth numercal examples, allows us to solve the equlbrum, provde ntuton and compare our results to those n prevous lterature. 10

13 Frst, we look at the expresson that makes usng a fully connected structure a best response to the rval usng fully connected as well, Γ Π (F, F ) Π (H B, F ). Usng Eqs. (9) and (16), t s gven by: Γ = [ B (q (F,F m ) )2 (q (H m B,F ) )2] + c f m M where the varables n Eq. l {ab,bc} f l (H B,F ) l L f l (F,F ), (19) (19) are evaluated at the untolled equlbrum wth route structures ndcated n parentheses. Eq. (19) shows that there are two effects drvng the adopton of fully connected over hub-and-spoke: the change n revenues, as a result of the change n the number of passengers n all three markets (frst bracketed term n the rght-hand sde), and the change n costs, due to varatons n the total number of flghts (second bracketed term n the rght-hand sde). Despte that s not possble to assess the sgn of Γ analytcally, the sgn of each term s ntutve. Hub-and-spoke networks are meant to save arlne costs through to a reduced number of lnks flown, thus, a natural expectaton s that the total number of flghts s reduced when movng from fully connected to hub-and-spoke (Brueckner, 2004). Is s, therefore, expected that the second bracketed term s negatve, so that t favors the adopton of a hub-and-spoke route structure over fully connected. The change n number of passengers n each market, however, may favor the pont to pont structure. To see ths, note that n the connectng market (AC n ths case), the passengers face a hgher full prce under H B than under F, because they ncur hgher travel delays and the cost of connectng (see Eq. (11)). As a result, the equlbrum number of passengers n the connectng market (for a gven route structure of the rval) should be hgher under a fully connected route structure. On the other hand, the full prce n the remanng two markets that are serve drectly under both structures (markets AB and BC) may be hgher or lower due to two counteractng effects: a hgher (lower) frequency under hub-and-spoke wth respect to fully connected n each lnk mples hgher (lower) congeston, but decreased (ncreased) schedule delay costs. Therefore, ts sgn s, a pror, ambguous. However, numercal analyses show that, for the consdered parameters, the number of passengers n these markets that are hgher under a hub-and-spoke route structure than under a fully connected structure, gven that the rval uses a fully connected structure; therefore, ths effect also favors hub-and-spoke route structures. For a monopoly and n absence of congeston, Brueckner (2004) already showed that ths expresson can be postve or negatve dependng on parameters, and that the owndemand senstvty parameter plays a key role. Therefore, a meanngful exercse s to analyze the effect of competton on the ndfference pont between F and H. purpose, the case wth ndependent products s useful. For ths When arlnes are ndependent, the only nterdependency s through congeston; thus, by lookng at cases wth E = 0, we can dentfy the ndfference pont n absence of strategc nteracton. Then, by varyng 11

14 the rato of substtutablty E/B keepng all other parameters constant, t s possble to assess the effect of competton on the choce of hub-and-spoke over fully connected route structures. In contrast to prevous studes that analyze route structure choce, an asymmetrc equlbrum wth both arlnes havng a hub-and-spoke route structure may arse because the hub locaton s endogenous. Fgure 2 shows the equlbra for a range of the own-demand senstvty B parameter (horzontal axs) and all possble values of the rato of substtutablty E/B (vertcal axs), for a partcular parameter constellaton and functonal forms (see Appendx A for detals). In our model, the second-order condtons nvolvng the cross dervatves do not hold globally, but we restrct the numercal analyss to the cases where they do hold. The lnes dvde the dfferent parameter regons wth a common set of equlbra, and we have set the tolls to zero to descrbe the unregulated equlbrum. Fgure 2 reveals that, for the chosen parameters, two set of equlbra arse: both arlnes usng fully connected route structure (F, F ), and both usng hub-and-spoke but n dfferent hubs (H x, H y ); t also reveals that there are regons where both sets of equlbra may arse (the regon between the two lnes). Fgure 2 also suggests that a hgher substtutablty between arlnes favors the choce of hub-and-spoke route structures, as the ndfference lnes are to the left of the ndfference pont for E/B = 0. 1,0 0,8 (F, F ) (H x, H y) 0,6 E B 0,4 (F, F ) & (H x, H y) 0,2 0, B Fgure 2: Untolled equlbrum n route structures. Man parameterzaton (see Appendx A). 12

15 Our results n Fg. 2 show that, when markets and arlnes are symmetrc and for the consdered parameters, the best response to the rval usng a hub-and-spoke route structure, s ether adoptng a fully connected or a hub-and-spoke route structure, but usng a dfferent arport as the hub. That s the reason why asymmetrc hub-and-spoke equlbra (H x, H y ), arse nstead of symmetrc hub-and-spoke equlbra (H, H). As the cost advantages that adoptng hub-and-spoke brngs can be exploted n a smlar way under symmetrc and under asymmetrc hub-and-spoke settngs, the man dfference between both structures comes from the change n number of passengers n the connectng market. In a symmetrc hub-and-spoke settng (H, H), the competton s drect n all markets; n an asymmetrc hub-and-spoke settng (H x, H y ), the connectng market of the rval s domnated (as t s served pont to pont). Ths gan from domnatng the rval s connectng market seems to be hgher than the loss of beng domnated n the own connectng market, whch explans why, gven that the rval s usng a hub-and-spoke structure, choosng a dfferent arport as the hub domnates choosng the same when consderng adoptng a hub-and-spoke structure. 9 As the purpose of the paper s to compare the untolled equlbra wth the welfare maxmzng stuaton, and analyze how to enforce t, the next secton studes the frst-best combnaton of route structure and output. 4. Welfare analyss We frst look at the welfare maxmzng output for a gven choce of route structure by arlnes, dervng the tolls that nduce that output choce. Thereafter, we study the socally effcent route structure equlbrum and whether these tolls are suffcent to acheve t as an equlbrum of the full game The symmetrc fully connected case In ths case, denoted (F, F ), both arlnes serve the markets wth a fully connected route structure. We look at a regulator that maxmzes unweghted socal surplus, wth the toll per-passenger n each market (τ m ) and the toll per-flght n each lnk (τ l ) as nstruments. Straghtforward calculatons yeld the followng expresson for socal welfare: [ ] SW (F,F ) B = 2 ((qm ) 2 + (qj m ) 2 ) + E q m qj m + [ π F + π F ] j + m M [ ] [ ] τ m q m + Tj m qj m + τ l f l + τj l fj l, (20) m M where the frst term n brackets s the consumer surplus, the second term s the arlnes proft, the thrd term s the revenue from per-passenger tolls, and the fourth term s the l L 9 We numercally check that choosng a dfferent arport as a hub domnates choosng the same arport as the rval n the whole parameter range,.e. not only n the regon where (H x, H y) s an equlbrum. 13

16 revenue from per-flght tolls. The frst-order condtons for welfare maxmzaton under fully connected route structures mply the followng prcng and frequency settng rules: SW (F,F ) q m = 0 p m = c q m M, (21) SW (F,F ) f l = 0 m M (q m + q m j ) Dm f l + q m gm f l = c f. (22) Note that the tolls cancel out, because they are only monetary transfers, and that we drop the ndex on the delay cost functon as t s the same for both arlnes, because we are lookng at a symmetrc route structure settng. Equaton (21) states that the fare should equal the margnal cost of a seat n all markets, and (22) states that, n every lnk, frequency should be such that the arlne s margnal cost per flght equals margnal benefts for all passengers. Comparng (7) wth (21), and (8) wth (22), we derve the tolls that maxmze socal welfare under (F, F ): τ m = q m B m M, (23) τ l = m M q m j Dm f l l L. (24) Ths s smply a per-passenger subsdy equal to the markup for each market, to elmnate the dead-weght loss n all markets, and a per-flght toll equal to the unnternalzed congeston for each lnk. Ths s a tradtonal result n the arport prcng lterature (e.g. Brueckner, 2005). The two nstruments above (Eqs. (23) and (24)) attan the socal optmum, f both arlnes exogenously choose fully connected structures. The optmal value for socal welfare, n ths fxed route structure equlbrum, s: SW (F,F ) = m M B 2 ((qm ) 2 + (qj m ) 2 ) + E q m qj m (f l + fj) l c f, (25) l L wth quanttes and frequences satsfyng (21) and (22) The symmetrc hub-and-spoke case Followng the same procedure as n Secton 4.1, straghtforward calculatons yeld the followng rules for welfare maxmzng prcng and frequency settng under (H, H) route structure (wth B as the hub arport n ths case): SW (H,H) q m = 0 p m = c q m {AB, BC}, (26) SW (H,H) q AC = 0 p AC = 2 c q, (27) 14

17 SW (H,H) f l = 0 m {AB,BC} (q m +q AC +qj m +qj AC ) Dm f l +(q m +q AC ) gm f l = c f. (28) Agan, n the optmum, the fare should equal the margnal cost n all markets, and frequences should be such that the arlne s margnal cost per flght equals margnal benefts for all passengers. Comparng frst-order condtons, we obtan the tolls that maxmze socal welfare under symmetrc hub-and-spoke route structures: τ l = m {AB,BC} τ m = q m B m M, (29) (q m j + q AC j ) Dm f l l {ab, bc}. (30) These are the suffcent nstruments when route structure s fxed to be hub-and-spoke for both arlnes. wrtten as: In equlbrum, the optmal value for socal welfare under (H, H) can be SW (H,H) = m M wth varables satsfyng (26)-(28) The asymmetrc cases B 2 ((qm ) 2 + (qj m ) 2 ) + E q m qj m l {ab,bc} (f l + f l j) c f, (31) We have shown n Secton 3.3 that also asymmetrc equlbra may arse, n partcular (F, H) and (H x, H y ). It s straghtforward to show that optmal prcng and frequency settng rules wll be a combnaton of the rules descrbed above ((21), (22), and (26) (28)). As a result, the tolls that maxmze welfare for asymmetrc equlbra wll also be a combnaton of the tolls above; for an arlne wth fully connected route structure, (23) and (24) should be charged, and for an arlne usng hub-and-spoke, (29) and (30). The dfference wll be that the tollng rules wll be evaluated at dfferent outputs, and that Eqs. (29) and (30) have to be adjusted f the hub s not B The optmal route structure We now look at the combnaton of route structure and output that maxmzes welfare. Agan, complexty prevents us from fully comparng socal welfare values analytcally. As n Secton 3, we combne analytcal results wth numercal examples to dentfy the equlbra and provde ntuton. Frst, we compare the choce of route structure by unregulated frms wth the socal welfare maxmzng choce, to dentfy the sources of potental neffcency. Consder the comparson only between the followng route structure equlbra: (F, F ) and (H A, H B ). We focus on the comparson between these partcular structures because the numercal analyss suggests that, for the consdered symmetry, those are the settngs that can be frst-best 15

18 optmal. To compare the socal optmum wth the untolled equlbrum, let the dfference between socal welfare n both settngs be SW (F,F ) SW (H A,H B ). The condton > 0 s necessary for (F, F ) to be the welfare maxmzng route structure settng, whle the condton Γ > 0 n Eq. (19), s suffcent for (F, F ) to be an equlbrum. Usng (25), and (31), we get: + c f = m M B 2 [ (q (F,F m ) )2 (q (H m A,H B ) )2] + B [(qj (F,F m ) 2 )2 (q m j (HA,HB ) )2] m M l {ab,ac} f l (H A,H B ) l L +E [q (F,F m ) qm j (F,F ) qm (H A,H B ) qm j (H A,H B ) ] + c f f l (F,F ) l {ab,bc} f l j (H A,H B ) l L f l j (F,F ), (32) where the varables n (32) are evaluated at the socal optmum for the gven route structure settng n parentheses. The comparson between Γ n Eq. (19), and n Eq. (32) sheds lght on the neffcency of route structures choce by proft maxmzng agents and makes mplausble that unregulated competton between arlnes wll always lead to the frst-best route structure. Frst, recall that there s a dfference n output between the two cases, as dscussed above, due to two effects: market power exerton and the presence of congeston externaltes. Ths clearly makes the varables of and Γ dffer. Even f the outputs were the same, n the socal welfare comparson there s a term nvolvng the cross senstvty parameter (E) that s absent n proft comparson;.e. a frm gnores the effect of ts choces on the consumer surplus derved by the compettor s passengers. Moreover, the arlnes relevant comparson s for a gven route structure of the rval, whch agan makes and Γ dverge. In a monopoly context, Brueckner (2004) shows that the choce of route structure by a monopoly arlne wll be based towards hub-and-spoke. In our problem, the dvergence between settngs s complcated because frequency settng for a gven number of passengers s dstorted by congeston effects, and, when arlnes are substtutes, both are dstorted by strategc effects. Therefore, whether competng arlnes are based towards hub-and-spoke cannot be assessed analytcally. A look at n Eq. (32) reveals that what drves whch route structure composton maxmzes welfare, at least between the symmetrc fully connected settng (F, F ) and the asymmetrc hub-and-spoke settngs (H x, H y ), s the cost advantages that hub-and-spoke may brng (last two terms on the rght-hand sde of Eq. (32)), versus the changes n the number of passengers n each market. Fgure 3 summarzes, for the same parameter regon used n Secton 3 (see Appendx A for detals), the welfare maxmzng route structure (when evaluated at the optmal output for those parameters). Recall that the frst-best settng n Fgure 3 s the one that maxmzes welfare, and t s not necessarly an equlbrum 16

19 of the tolled competton. We analyze whether and when the frst-best settng and the (tolled) equlbrum concde n the followng secton. 1,0 0,8 (M f ) 0,6 E B (H x, H y) 0,4 (F, F ) 0,2 0, B Fgure 3: Welfare maxmzng route structures. Man parameterzaton (see Appendx A). Fgure 3 suggests that, for the chosen parametrzaton, the route structure confguraton that maxmzes welfare, when all markets are served by both arlnes, s ether symmetrc fully connected (F, F ) or asymmetrc hub-and-spoke (H x, H y ). A smple comparson between Fgures 2 and 3 confrms that the outcome of the unregulated competton may lead to route structure equlbra that are dfferent from the effcent one. Fgure 3 also suggests that the hgher the substtutablty between arlnes, the more lkely s (H x, H y ) to be a more effcent route structure equlbrum than (F, F ). It stll brngs cost savngs and frequency benefts, but t s less essental that all arlnes are present on all routes. One of the effects that favors the fully connected symmetrc equlbrum over the asymmetrc huband-spoke structures, s the absence of connectng passengers, because they have a hgher margnal cost per seat and face a hgher full prce. In an asymmetrc hub-and-spoke settng (H x, H y ), the number of connectng passengers decreases as the arlnes are perceved as closer substtutes, because n every connectng market of one arlne, the rval provdes a drect servce prced at margnal cost (because we are lookng at the frst-best settng). Therefore, when products are close substtutes, the number of connectng passengers s low, and the gans from lower total costs due to reduced total frequency domnate. Note that 17

20 ths s not possble to acheve under symmetrc hub-and-spoke (H, H). It s also worth notng that when products are ndependent, asymmetrc settngs may be welfare maxmzng. Ths occurs when demand s low (rght end of the horzontal axs n Fgure 3), where (H x, H y ) s the most effcent settng. The ntuton behnd ths s that cost advantages from reduced total number of flghts that hub-and-spoke brngs n ths regon domnates, and that total congeston costs may be lower under (H x, H y ) than under a symmetrc hub-and-spoke settng, where all flghts ether take off or land at the hub arport. Asymmetrc hub-and-spoke structures can beneft non-connectng passengers, as one of the arports wll be less congested compared to when t s the hub of both arlnes. Addtonal numercal examples, not shown here, reveal that only when arlnes are perceved as ndependent and there s no congeston, symmetrc and asymmetrc huband-spoke structures yeld the same welfare, for the consdered parameters. On the other hand, when products are perfect substtutes, the socal optmum cannot have two arlnes usng dfferent route structures ((H x, H y ) and (F, H)). Ths s because full prces must be the same for all arlnes that are servng the market, but also should be set at margnal socal cost. As margnal socal costs, under dfferent route structures, are dfferent n at least one market, these two constrants make an asymmetrc route structure settng ncompatble wth welfare maxmzaton when products are perfect substtutes (E/B = 1). What s optmal, nstead, s to have regulated monopolzed markets. Ths result s drven by that, for a sngle market, hgher welfare s acheved under the full regulaton of a monopoly than of perfect substtute competng arlnes. Ths s because we are lookng at a regulator who solves the congeston neffcency and the market power exerton through tolls; therefore, there s no dead-weght loss regardless of the number of frms. In addton, the frequency set by a fully regulated monopoly arlne s hgher than for a fully regulated arlne n olgopoly, as demand s dvded between frms, thus schedule delay costs wll be lower. Ths s what favors a monopoly. When dfferentaton s weak (B E), the expanson of demand generated by a new frm may overweght the schedule delay cost advantages of a monopoly, and competton wll brng hgher welfare. 10 Ths may also hold when arlnes are close substtutes, as Fgure 3 reveals: n the parameter regon M f, t s welfare maxmzng to have a regulated monopoly arlne servng the three markets wth a fully connected route structure. As already shown by Brueckner (2004), dependng on parameters, t may be more effcent from a socal welfare pont of vew, to have a regulated monopoly usng fully connected route structure (M f ) or servng the market wth hub-and-spoke Despte havng a dfferent model, the ntuton s the same as n Basso (2008). 11 For the parameters of our man case, the value of the own-demand senstvty parameter that makes a hub-and-spoke route structure more effcent than a fully connected structure under a regulated monopoly s B = 30.4 (not shown n Fgure 3). 18

21 We now turn to the analyss of how to enforce the frst-best descrbed n ths secton. Ths s, can the frst-best settng be a toll-decentralzed equlbrum? 5. Suffcent nstruments for socal welfare maxmzaton 5.1. Frst-best analyss In order to study whether the two prcng nstruments descrbed n Secton 4 algn arlne choces wth welfare maxmzaton, we numercally examne the equlbrum of the game when the regulator charges the optmal tolls condtonal on the frst-best route structure. In other words, we derve the outcome of the game n each of the regons of Fgure 3, when the regulator charges the tolls that nduce the optmal output for the gven welfare maxmzng route structure. For example, n the parameter regon denoted by (F, F ) n Fgure 3, the regulator set the tolls accordng to rules (21) and (22); f the equlbrum that results from chargng these tolls s wth both arlnes choosng fully connected route structure, the frst-best s acheved as the charges ensure optmal outputs. Conversely, f the equlbrum wth the optmal charges n the parameter regon where (F, F ) maxmzes welfare s not wth both arlnes choosng fully connected route structure, we can conclude that the two prcng nstruments are not suffcent n ths case. Ths s because any other charge, that may nduce the optmal route structure equlbrum, wll not nduce the optmal output. Fgure 4a compares the untolled equlbrum n Fg. 2 wth the welfare maxmzng settng n Fg 3, n terms of route structure. It reveals that the ratonale for the charges s not always the same: they can be requred only to correct output settng, to correct smultaneously output and route structure choce, and n order to correct market structure as well. The whte areas represent the cases where the arlnes route structure equlbrum s the same as the frst-best, and only output correctons are needed. The lght gray areas are where the route structure equlbrum from untolled competton s dfferent from the effcent one, and the tolls are requred to nduce arlnes to choose both the welfare maxmzng outputs and route structures. The M regon, n dark gray, ndcates that welfare maxmzaton requres tolls that exclude one arlne from the market, as a fully regulated monopoly would be optmal. We use the labels to ndcate the effcent route structure when t dffers from the one adopted by unregulated competng arlnes. Let us frst dscuss the dfference between the route structure n the untolled equlbrum versus that n the optmum (later we wll dscuss whether tolls alone can decentralze the optmum). Fgure 4a shows that the result that a monopoly arlne exhbts a bas towards hub-and-spoke route structure does not fully carry on to competng arlnes. Ths s, no longer whenever (H x, H y ) s welfare maxmzng, t s also an equlbrum of the untolled competton. For the chosen parametrzaton, (H x, H y ) s optmal but the untolled equlbrum s (F, F ) when own-demand senstvty to prce changes and substtutablty are 19

22 1,0 1,0 0,8 (M f ) 0,8 0,6 E B 0,4 (H x, H y) 0,6 E B 0,4 ω = 0.8 ω = 0.85 ω = 0.9 0,2 (F, F ) 0,2 0, B 0, B (a) Tolls ratonale. (b) Tolls relatve effcency. Fgure 4: Frst-best tolls ratonale and relatve effcency of output-based tollng. Man parameterzaton (see Appendx A). not too low (roughly, n the trangle where B s lower than 18 and E/B between 0.4 and 0.8 n Fgure 4a). The reason why n that area we fnd (F, F ) n the untolled equlbrum s that, when changng from a fully connected to a hub-and-spoke route structure, the full prce n the connectng market ncreases. Therefore, when demand s relatvely senstve to prce changes (low B), the proft loss n the connectng market s larger than the cost benefts and the equlbrum s wth (F, F ). However, ths demand reducton n the arlnes connectng market does not necessarly harm welfare. In ths area, we fnd (H x, H y ) n the optmum because the cost advantages that hub-and-spoke structures brng can be exploted wthout havng a large number of connectng passengers. Under (H x, H y ), n each arlne s connectng market the compettor offers a drect servce wth a lower full prce. As demand s relatvely senstve to prce changes and substtutablty s not low, the number of connectng passengers s low. Ths s only possble wth arlnes adoptng dfferent arports as ther hub, as otherwse the number of connectng passengers would not necessarly decrease. The opposte, (F, F ) beng effcent but untolled arlnes choosng (H x, H y ), occurs when substtutablty s not hgh (below 0.4 n Fgure 4a) and own-demand senstvty wth respect to prce changes s low (hgh B). The results also ndcate that a nave regulator, who observes the unregulated equlbrum and set the tolls based on the then observed route structure, may not always acheve the frst-best. The regulator should realze whenever the observed equlbrum s not effcent n terms of route structure (the gray regons), and nduce arlnes, va tolls, to change the way they serve the markets. 20

23 A man result of our numercal analyses s that the frst-best cannot always be enforced by usng the arlne- and market-specfc per-passenger tolls together wth the arlne- and lnk-specfc per-flght tolls desgned to nduce the optmal outputs of the frst-best route structures. Thus, the sub game-perfect equlbrum s not always effcent, even when the regulator can perfectly dscrmnate between arlnes and when t has no budget constrants. The shaded area n Fgure 4b represents the parameter range where the toll nstruments descrbed n the prevous sectons cannot decentralze the frst-best. Ths regon has arlnes adoptng fully connected route structures nstead of the frst-best settng (H x, H y ). Ths s due to the asymmetry of the toll structure: to enforce (H x, H y ), the regulator must gve a subsdy n each market that ncreases wth the frm s number of passengers, and a per-flght toll on the two routes that are flown by each arlne. Gven ths toll confguraton, adoptng a hub-and-spoke route structure may be strctly domnated by the fully connected strategy, because the ntended connectng market can be served drectly wthout payng a per-flght toll. Dong ths may ncrease revenue due to an ncreased number of passengers, because the full prce n that market s lower when served drectly. In the shaded regon of Fgure 4b, ths effect domnates the potental cost advantages that the frm would have from adoptng a hub-and-spoke structure, n presence of tolls ntended for a hub-and-spoke settng. 12 To reach the frst-best outcome n these cases, an addtonal nstrument s therefore requred. 13 Ths also mples that more nformaton s needed to attan the frst-best, as the varables usually needed for frst-best tollng (e.g. margnal external cost) are not enough to assess dscrete changes n welfare under dfferent route structures. A natural queston that follows from the above results s how bg the loss n welfare s, when chargng the output-based tolls and not achevng the frst-best route structure. Fgure 4b also shows the relatve effcency of such tolls (ω), as the percentage of the maxmum welfare gan that can be obtaned (the frst-best settng n Secton 4) usng the untolled equlbrum as the reference scenaro for the welfare level. The relatve effcency ranges from 1 n the whte areas of Fg. 4b where the tolls are suffcent nstruments to acheve the frst-best; to 0.77, the lowest possble relatve effcency of the output-based tolls, n the darkest regon of the fgure. Although, n our model, the regulator does not have drect control on the number of arlnes, he can prce an arlne out of one market through the tolls. To do ths, one arlne 12 We do not fnd n the numercal analyses that the equlbrum wth tolls has arlnes adoptng hub-andspoke route structure n a parameter regon where fully connected s the welfare maxmzng structure. 13 For example a arbtrarly hgh per-flght toll n the connectng market of each arlne can act as a barrer to fully connected structures. As ths charge s not pad n equlbrum, because the arlnes adopt a hub-and-spoke structure, t does not nduce any neffcency n output, but only the ncentves to adopt the optmal route structure. A drect restrcton to an arlne to fly from those arports s also a suffcent addtonal nstrument for these cases. 21

24 should receve the per-passenger (market power) subsdy that corresponds to the monopoly output, and face no congeston toll. Ths s because a monopolst perfectly nternalzes congeston externaltes. The other arlne should face a prohbtve toll that removes the ncentves to become actve. Note that the latter may not always be needed; n some cases, a large output choce by the subsdzed arlne may be enough to shft the rval s demand to levels that are not proftable or non-postve, gven the congeston delay costs. Fnally, addtonal numercal analyses (not shown) show that the boundares ndcated n Fgure 4 change when parameters are changed, but the man qualtatve results hold Second-best analyss The results n Secton 5.1 requre the regulator to be able to gve subsdes to arlnes, and, n some cases, to exclude one arlne out of the market. Ths s arguably close to mpossble to carry out n real networks, and, nstead, a regulator wll most lkely be constraned to charge non-negatve tolls. Ths secton consders the realstc case where only non-negatve tolls can be charged, and compares the second-best optmal route structure equlbrum wth the frst-best equlbrum. An mportant queston s, agan, whether the second-best tolls are able to nduce the desred (second-best) outcome also n terms of route structure. As we normalze arport costs to zero, the frst-best toll per passenger we found above s equal to a market power subsdy, and therefore t s always negatve (see Eqs. (23) and (29)). The frst-best per-flght toll s always non-negatve (un-nternalzed congeston, see Eqs. (24) and (30)). It s, therefore, expected that n the second-best case we now study, the per-flght tolls are adjusted downwards to compensate for the lack of subsdes, and that n some parameter regon they may even become (constraned to) zero. Ths would be the case f the congeston externalty s suffcently low compared to the justfed market power subsdy. 15 Fgure 5 shows the second-best optmal settng for the same parameter constellaton and functonal forms as n Sectons 3 and 4. The sold lne dvdes the dfferent second-best optmal regons, whch are agan (F, F ) or (H x, H y ), and the dashed lne s the analogous dvsonal lne for the frst-best case. Ths allows for a comparson between the second- and frst-best equlbra. 14 We assess how the arlnes untolled equlbrum n route structure changes and whether the frst-best settng can be decentralzed wth tolls for dfferent parameters of the delay functon, the arlne cost functon, and the passenger values of tme. The changes n route structure equlbra follow the ntuton provded by prevous studes (e.g., Brueckner, 2004): hub-and-spoke route structures are favored by hgher values of the per-flght fxed cost c f, lower fxed margnal cost per seat c q, hgher dsutlty of schedule delay γ, and lower congeston. 15 Pels and Verhoef (2004) analyze ths usng a sngle orgn-destnaton par. They fnd that n some cases the second-best polcy s to set the tolls equal to zero. 22

25 1,0 0,8 X (H x, H y) 0,6 Frst-best E B 0,4 (F, F ) 0,2 Second-best Y 0, B Fgure 5: Second-best optmal route structures and comparson wth the frst-best case. Man parameterzaton (see Appendx A). Fgure 5 shows that, when subsdes are not feasble, fully connected route structures are favored when the degree of substtutablty (E/B) s low and own-demand senstvty s hgh (low B), and asymmetrc hub-and-spoke route structures are favored when the opposte apples, n a smlar manner as n the frst-best case. However, there s a regon denoted X where (F, F ) s second-best optmal whereas (H x, H y ) s frst-best optmal, and vce versa (the Y regon). The dfference s caused by the fact that n the second-best cases, there are dead-weght losses due to the lack of subsdes. Competton under both arlnes usng fully connected s drect n all three markets, whereas n the asymmetrc hub-and-spoke equlbrum there s one market where one arlne has an advantage over the other (offerng a drect flght). In the area X, where substtutablty (E/B) s hgh and demand s more prce senstve (low B), the drect competton that a fully connected route structure brngs may decrease dead-weght losses by more than under an asymmetrc hub-and-spoke structure, and t s more favored than the case where all neffcences are dealt wth through prcng. In the area Y, where demand s less prce senstve (hgher B) and substtutablty (E/B) s low, ths effect s decreased and the dfference n number of passengers becomes smaller; as a result, the cost advantages of hub-and-spoke structures become more attractve. 23

26 The results also show that the monopoly regon does not exst for the consdered parameters, as the dead-weght losses from monopoly prcng are no longer beng corrected through the subsdy; t s better to regulate a duopoly when tolls are constraned to be non-negatve. Fgure 6 compares the second-best optmal route structure equlbra wth the untolled equlbra, and t reveals that also the ratonale for the second-best charges may nclude the desre to change the route structure. The whte areas agan ndcate the cases where the route structure n the untolled equlbrum s the same as the second-best optmum, and tolls only correct for output neffcences. The lght gray and dark gray regons show where the neffcency occurs both n route structures and n outputs, and therefore tolls may be requred to correct both. 1,0 0,8 (H x, H y) 0,6 E B (H x, H y) 0,4 0,2 (F, F ) 0, B Fgure 6: Second-best tolls ratonale and decentralzaton of the second-best optmum. Man parameterzaton (see Appendx A). Fnally, where the second-best optmal route structures n Fgure 6 are assumed to apply, we also study whether they are decentralzed by second-best tolls, n order to study whether the per-flght tolls are suffcent nstruments to acheve the second-best outcome n route structures shown n Fgure 5. As explaned above, these tolls mght be zero f the congeston externalty s suffcently low compared to the market power exerton by arlnes. Therefore, t follows that n the regons where second-best tolls are zero and the 24