Analysis of high-speed rail and airline transport cooperation in presence of non-purchase option

Transcription

1 J. Mod. Transport. (208) 26(4): Anaysis of high-speed rai and airine transport cooperation in presence of non-purchase option Kimitoshi Sato Yihsu Chen 2 Received: 5 September 207 / Revised: 9 Juy 208 / Accepted: 8 August 208 / Pubished onine: 6 September 208 Ó The Author(s) 208 Abstract We study cooperation between the airine and high-speed rai (HSR) sectors by formuating their joint profit as a maximization probem using a mutinomia ogit choice mode in a three-node setting. We aow the nonpurchase option as an outside option avaiabe to consumers. The demand for each choice is not ony a function of the price but aso the service quaity, such as the tota trip time, frequency of service, and ease of connecting from the hub to a nearby HSR station. As a resut, the foowing findings are presented. First, regardess of the service quaity of either sector and the non-purchase option, cooperation decreases the tota voume of the domestic market of a country. Second, when the attractiveness of the outside option is high, the HSR and air sectors can prevent a arge reduction in the tota voume by cooperation in the connecting market. However, this is not the case in the domestic market. Third, if the non-purchase quaity in the domestic market is high, then cooperation increases the socia wefare of the whoe market. If the non-purchase quaity is ow, then cooperation increases the wefare of the whoe market ony in cases where the number of potentia customers in the connecting market is reativey arge. We & Kimitoshi Sato k-sato@kanagawa-u.ac.jp Yihsu Chen ychen225@ucsc.edu 2 Facuty of Engineering, Kanagawa University, Rokkakubashi, Kanagawa-ku, Yokohama, Kanagawa , Japan Department of Technoogy Management, University of Caifornia, Santa Cruz, 56 High Street, Santa Cruz, CA 95064, USA aso show the effect of improving air rai service quaity on each market share and on the tota profit. Keywords Integration Competition Airine Highspeed rai Mutinomia ogit mode Introduction Traditionay, high-speed rai (HSR) has been one of most efficient ways to trave between an origin and destination which are ess than 000 km apart, or when the trave time is ess than.5 h [ 3]. Therefore, HSR is a de facto competitor of the air sector as it provides a service which otherwise woud be provided by an airine. For exampe, with the introduction of an HSR in Taiwan in 2007 inking the two argest cities, Taipei and Kaohsiung (248 km apart), the domestic airine industry experienced a significant drop in market share and a decrease in profit [4]. However, as auded to by Givoni and Banister [5], the reationship between airines and HSR is far from that of pure competitors. In particuar, they argue that the existence of HSR can compement the airine industry by providing services from a node within an airine network to nearby cities. In fact, this HSR airine cooperation is especiay economicay desirabe for hub spoke-type networks which are common in most countries. With most airports ocated outside of city centers, the integration of HSR with oca train networks can further enhance the benefits associated with HSR airine cooperation. Another often cited advantage of HSR airine cooperation is the environmenta benefit associated with a reduction in CO 2 emissions [6]. As HSR airine cooperation is a reativey new concept, there are ony a imited number of cases/routes where such 23

2 232 K. Sato, Y. Chen cooperation has been impemented, most of which can be found in Europe. One exampe is the air rai services provided by Lufthansa and Deutsche Bahn that ink the airine hub in Frankfurt to nearby cities, incuding Stuttgart, Coogne, and Bonn. These three cities are ocated between 30 and 50 km from Frankfurt with commuting times of min. Daiy, the numbers of trains running from Frankfurt to Stuttgart, Coogne, and Bonne are 23, 43, and 27, respectivey. Passengers traveing via Frankfurt to one of these three cities are provided with a combo ticket comprising an airine ticket to Frankfurt and an HSR ticket from Frankfurt to their fina destination. Such cooperation provides two obvious benefits. First, uggage wi be deivered directy to the fina destination, and passengers can avoid the inconvenience of retrieving uggage at the airport and then carrying it during transit. This coud aso imit the possibe time deay caused by uggage transit when the airport crew need to hande arge voumes of uggage during rush hours. Second, HSR in these three cities is integrated with the oca train networks, therefore eiminating the need for connections invoving other forms of ground transportation. Whie HSR airine cooperation is appeaing, its impementation is subject to a number of chaenges. Perhaps, the most important one is the fact that airines and HSR are owned by separate entities, who are operated under different objectives and by different institutions. Traditionay, they see each other as rivas and compete for the same consumers. After Tokyo s successfu bid to host the 2020 summer Oympics, discussions have begun on the use of Shizuoka Airport as a hub through which passengers from other countries coud visit Tokyo and Osaka during the Oympics. The discussions have incuded two key issues. One is that the two major airports serving the Tokyo area, Narita and Haneda, are aready operating at cose to their maximum capacity during busy seasons. Any increase in demand during the Oympics woud ikey push these airports over their maximum fight capacities, eading to deays and other probems. Second, in the event of disruptions caused by earthquakes or other natura hazards, HSR airine cooperation woud provide a much-needed aternative to ensure reiabe transportation during the Oympics. However, even during initia discussions, there have been a number of issues raised by the two main entities invoved: the Japan Raiway Company (JR) and Shizuoka prefecture. In particuar, JR has argued that it presents a major engineering chaenge and is technicay impossibe to construct an underground faciity under the current ocation of Shizuoka Airport to ink the airport to the HSR network. This suggests the Japanese government shoud not rey on the two parties to vountariy engage in the discussion and impementation of HSR airine cooperation. Another possibe expanation of why there is itte HSR airine cooperation in practice is that the benefit and tradeoffs of such cooperation are not we understood. Competition between the airine and HSR industries has been an active research area for years [7 2]. In particuar, two papers concuded that the introduction of a new HSR network woud have a negative impact on the airine industry by decreasing its market share [7, ]. Ader et a. [8] deveoped an amost compete game engineering mode and concuded that the European Union (EU) coud benefit from HSR airine cooperation. Yang and Zhang [9] studied the competition between these two sectors by formuating the objective of HSR as a weighted sum of its profit and socia surpus. Their paper shows that increasing the weight on socia surpus woud ower the price of both HSR and airines, thereby benefitting consumers. This is not a surprising resut, as the HSR sector incudes consumer surpus in its objectives. The paper then conducts a comparative statistica anaysis of the airport access time, rai speed, and other factors. An empirica study by Behrens and Pes [0] focuses on the London Paris market and finds that there was intense competition between airines and HSR. Their paper further identifies that the frequency, trave time, and ease to connect to other networks are the factors which determine traveers preference. On the other hand, there is reativey itte iterature on the cooperation between these two sectors [5, 3 6]. The two papers which are most reevant to our present study are by Socorro and Viecens [5] and Jiang and Zhang [3]. Both papers use a simpified three-node network in which a non-domestic origin city is inked to a fina domestic destination through a domestic hub and consider the cases of whether the airport is capacity constrained or not. However, Socorro and Viecens [5] appied a prescribed rue to ration airport capacity when there is a shortage of capacity. In contrast, Jiang and Zhang [3] endogenize the decision of aocating scarce airport capacity between different markets. Their paper further anayzes the impact of traffic frequency, vertica differentiation between nodes, price easticity, and heterogeneous passenger types on the market outcomes. In this respect, the framework deveoped by Jiang and Zhang [3] is more compete and aows for the consideration of more factors which have practica reevance to consumers preference. Our paper aso reies on a simpe three-node network to examine the market outcomes of HSR airine cooperation with consideration of airport capacity. However, our work differs from Jiang and Zhang [3] and Socorro and Viecens [5] in a number of ways. First, we depoy a mutinomia ogit mode (MNL) to represent consumers trave demand. Thus, in contrast to Jiang and Zhang [3], we consider factors that are crucia for determining the demand for different transportation modes, such as frequency, trave 23 J. Mod. Transport. (208) 26(4):23 254

3 Anaysis of high-speed rai and airine transport cooperation in presence of non-purchase time, cost, time to airport or HSR station, and conformabiity, and aow them to be reated to the demand nonineary. In other words, our approach does not require the margina effect of these factors on the demand to be constant. Second, our approach to modeing the demand aows non-purchase as an outside option avaiabe to consumers. That is, when their maximum wiingness to pay is ess than the cheapest ticket prices, they can decide to cance the trip. Therefore, our mode can more reaisticay refect the decision-making process of consumers. Without the non-purchase option, an anaysis might overestimate the market shares of both transportation modes. Recenty, Xia and Zhang [6] aso considered competition and cooperation between HSR and airines in a threenode setting. There are some differences with our mode. They assume that () the air transport and HSR are verticay differentiated, (2) the demand function is a function of both fares and the tota trave time, (3) there are two airines operating in the internationa market, and (4) the hub airport capacity is constrained. Unike their mode, we assume that the demand function is defined as an MNL mode, so that air transport and HSR are horizontay differentiated. The MNL mode is widey used in estimating trave demand (see [7]). The popuarity of MNL stems from the fact that it is anayticay tractabe, reasonaby accurate, and easiy estimabe using standard statistica techniques [8]. Since the service quaity for each mode and non-purchase option is incorporated as a inear function in the MNL demand, we can aso anayze the effect of trave time on HSR airine cooperation through a sensitivity anaysis of service quaity. Moreover, in our mode, the operating cost changes depending on the service quaity. This is a more reaistic assumption than in the above papers. However, the present paper does not consider competition in the internationa market and capacity constraint. Athough these are important issues in practice, we focus on the anaysis of the effect of service quaity and the non-purchase option on the transport operator s profits, consumer surpus, and socia wefare. Our contributions are summarized as foows. First, in an HSR-accessibe market, we show that rai fare increases as the service quaity of HSR increases (Proposition 3.2), which agrees with the resuts of previous papers (e.g., [9, 6]). However, airfare is not affected by the service quaity of HSR, which differs from the concusions of the existing iterature (e.g., [9, 6]). This is due to the independence of irreevant aternatives (IIA) in the MNL. Second, we find that when air transport and HSR cooperate, transport operators charge a higher fare in HSR-accessibe markets and the air air connection market increases (Proposition 4.2), which has aso been shown in Xia and Zhang [6]. However, airfare in HSR-inaccessibe markets is not affected by cooperation, whie Xia and J. Mod. Transport. (208) 26(4): Zhang [6] show that when air transport and HSR compete, the network carrier may charge excessivey high airfares. The difference between the resut of the present study and Xia and Zhang may be due to the choice of avaiabe transport aternatives in the connecting market. Xia and Zhang [6] assume that both air rai and air air connections are avaiabe in the HSR airine competition case. However, we assume that the air air transfer is the ony avaiabe option, which is the same as in Socorro and Viecens [5] and Jiang and Zhang [3]. We separate the air rai transfer demand into the HSR-inaccessibe and HSR-accessibe cases. Finay, we show that when the nonpurchase quaity in HSR-accessibe markets is reativey high, socia wefare increases with HSR airine cooperation (Proposition 4.7). This resut has not been shown in previous studies. Foowing Xia and Zhang [6], the comparison of resuts is summarized in Tabe. The remainder of the paper is organized as foows. In Sect. 2, we introduce the notation and assumptions used in this paper. In Sect. 3, we formuate an air and rai mode for the competition and cooperation cases, and derive the optima prices for both sectors. In Sect. 4, we study the effect of cooperation on the tota market voume and socia wefare for each market by comparing the competition and cooperation cases. In Sect. 5, we present numerica resuts to evauate the effect of coordination on the whoe market. Finay, Sect. 6 concudes the paper with further comments. 2 Notations Foowing Jiang and Zhang [3], we consider a network structure in which there are three cities (A, B, and H) with inter-city transport services, AH and HB, being connected by ony two inks (Fig. ). The AH route is operated ony by the air sector, whie HB is served by both airine and HSR operators. In addition, an airine serves the AB market using a hub-and-spoke strategy with H as its hub. That is, there is no direct fight service in the AB market. Let M i [ 0 be the number of potentia customers in market i where i ¼ ; 2; 3 indicate the markets AH, HB, and AB, respectivey. The sizes of these markets are determined from the city s popuation or annua number of passengers from the city. We define the set of fare casses offered by the air and HSR operators in market i as A i and When there is a direct fight service in the AB market, the network structure is caed a fuy connected (point-to-point) network. Recenty, Jiang and Zhang [9] showed theoreticay that HSR entry woud affect airines network structure such that they move from a point-to-point to a hub spoke network. Their resuts provide a rationae for our mode set-up using a hub spoke structure. 23

4 234 K. Sato, Y. Chen Tabe Comparison of resuts between our paper and the existing iterature J&Z [3] X&Z [6] Our mode Increasing rai speed forces airine to charge ower fares Yes Yes No Increasing rai speed aows HSR to charge higher fares Yes No Yes Higher airfare in HSR-inaccessibe market when air and HSR compete N.A. Yes No Higher airfare in HSR-accessibe market when air and HSR cooperate N.A. Yes Yes Higher HSR fare in HSR-accessibe market when air and HSR cooperate N.A. Yes a Yes Higher air air fare in air air connecting market when air and HSR cooperate N.A. Yes Yes Higher air rai fare in air rai connecting market when air and HSR cooperate N.A. Yes N.A. Increasing rai speed decreases air shares N.A. N.A. Yes Increasing rai speed increases HSR share N.A. N.A. Yes Higher traffic in HSR-accessibe market when air and HSR compete Yes N.A. Yes Higher traffic in air air connecting market when air and HSR cooperate Yes N.A. Yes Higher vauation of consumer s preference eads to ower traffic N.A. N.A. Yes Higher SW when air and HSR cooperate under higher NP quaity in HSR-accessibe market N.A. N.A. Yes J&Z¼Jiang and Zhang [3], X&Z¼Xia and Zhang [6], N.A.¼Not addressed, SW¼Socia wefare a This reation hods in the ong-hoe case, but is ambiguous in medium-hau case A Air Fig. Three cities network H R i, respectivey. The set of a services in market i is denoted by N i ¼A i [R i. We use an MNL mode to cacuate the probabiity of a consumer seecting a particuar trave mode. The desirabiity of a particuar trave mode under our mode settings can be determined from the fare price, trave time, frequency, and other attributes. Let f i;j be the price of service j in market i, and f i ¼ff i;j g j2n i be the vector of prices for a services in market i. The consumer utiity function for service j in market i is defined by U i;j ¼b i;j b i f i;j þ j ; i ¼ ; 2; 3; j 2N i ; ðþ U i;0 ¼u i;0 ; i ¼ ; 2; 3; ð2þ where b i;j characterizes the quaity of the service, b i [ 0 represents the price sensitivity parameter, j is a mean-zero random component, and u i;0 is the utiity associated with an outside aternative. The quaity of service b i;j is typicay modeed as a inear function of its attributes, i.e., b i;j ¼ a T x i;j, where a is a vector of parameters, and x i;j is a vector of attribute vaues for option j in market i. The Air HSR B service quaity of the air sector in market 3 is assumed to aso be affected by the connection time at the airport. The term j is assumed to be an independent identicay distributed (i.i.d.) random variabe with a Gumbe distribution that has cumuative density function FðxÞ ¼expf expf ð x þ cþgg, where c is Euer s constant, and is the scae parameter. The mean and variance of j are 0 and 2 p 2 =6, [ 0, respectivey. The probabiity that customers in market i seect a service j is given by e ðbi;j b if i;jþ p i;j ðf i ÞP U i;j ¼ max U i;j ¼ ; j2n i [f0g Pj2N i e ðbi;j b if i;jþ þ e u i;0 ð3þ and the probabiity of non-purchase is given by e u i;0 p i;0 ðf i ÞP U i;0 ¼ max U i;j ¼ : j2n i [f0g Pj2N i e ðb i;j b i f i;j Þ þ e u i;0 ð4þ Using the probabiity of seecting option j defined in Eqs. (3) and (4), the expected demand for mode of transport j in market i, d i;j, is cacuated as the product of the number of potentia customers and the probabiity of seection. That is, d i;j M i p i;j. We now consider the cost function. The cost function C i;j ðþ is defined as a function of the demand and consists of the variabe and fixed costs: C i;j ðd i;j Þ¼c i;j ðb i;j Þd i;j þ I i;j ðb i;j Þ; i ¼ ; 2; 3; j 2N i ; where c i;j ðb i;j Þ is variabe cost, and I i;j ðb i;j Þ is fixed cost. Note that the variabe and fixed costs are aso a function of 23 J. Mod. Transport. (208) 26(4):23 254

5 Anaysis of high-speed rai and airine transport cooperation in presence of non-purchase the service quaity b i;j. We assume that c i;j ðb i;j Þ is increasing with service quaity b i;j. For simpicity of notation, we write c i;j and I i;j instead of c i;j ðb i;j Þ and I i;j ðb i;j Þ, respectivey. 3 High-speed rai and airine mode In this section, we first consider an air and rai competition probem (foowed by the cooperation cases) and derive the optima prices for both sectors. 3. Competition case In the competition case, the air and HSR sectors compete for the route HB, and the air sector acts as a monopoy in markets i ¼ (AH) and i ¼ 3 (AB). 2 Thus, the set of avaiabe transportation modes in the markets is N ¼A, N 2 ¼A 2 [R 2 and N 3 ¼A 3, and R ¼R 3 ¼;. With the above cost and demand information, the maximization probem of the air sector is as foows: V a max v a ðfþ ¼ X3 X ffi;j f d i;j C i;jðdi;j Þg; ð5þ a i¼ j2a i where V a denotes the maximum expected profit of the air sector at equiibrium, f ¼ff i;j g for a i ¼ ; 2; 3; j 2N i is the vector of ticket prices for a markets, and f a ¼ff i;j g for a i ¼ ; 2; 3; j 2A i is the vector of air prices. The optima price and expected demand for service j in market i in the competition case are denoted by fi;j and di;j ¼ M ip i;j, respectivey. The maximization probem for HSR is given by V r max f 2;r v r ðf 2 Þ¼ X j2r 2 f 2;j d 2;j C 2;jðd 2;j Þ; ð6þ 2 In the absence of HSR airine cooperation, athough there are some consumers who are wiing to trave from A to B using the route HB by HSR and the route AH by air (we refer to this as itinerary ar ), we assume that the air sector acts as a monopoy in the connecting market. This assumption is vaid because of the foowing: () When a customer is searching for airine tickets for route AB using a trave search engine, the itinerary ar rarey appears in the search resuts, especiay when the HSR station is not ocated in the airport. Thus, most customers choose the itinerary with connecting fights and earn air mies or points. (2) The itinerary ar seems to be preferred by customers who trave from A to B through the connecting city H and want to stay for a coupe of days at city H. However, trave search engines (e.g., Skyscanner or Kayak) offer stopovers or muti-city fight options to customers. Thus, customers can reduce their costs by using this option, and the demand for the itinerary ar woud be very ow. For these reasons, we regard the demand for HSR aong route AH and the demand for air aong route HB separatey. J. Mod. Transport. (208) 26(4): where V r denotes the maximum expected profit of the HSR sector at equiibrium, f 2 ¼ff 2;j g for a j 2A 2 [R 2, and f 2;r ¼ff 2;j g for a j 2R 2. The profit functions v a and v r are not concave in f a and f 2;r (see [20]), and this poses probems when finding numeric soutions for the modes. However, as suggested by Dong et a. [2], a one-to-one reationship between the price and market share aows us to reformuate the probem by using the market share as the decision variabe. In particuar, the ratio of the market shares p i;j =p i;0 can be expressed as a function of the attributes as we as the utiity of the outside aternative, p i;j =p i;0 ¼ expfðb i;j b i f i;j u i;0 Þ=g. Thus, we obtain the price as a function of the ratio of market shares: f i;j ¼ b i;j u i;0 og p i;j : ð7þ b i p i;0 Here we define a vector of probabiities as p ¼fp i;j g for a i ¼ ; 2; 3; j 2 S i ða i [R i Þ, p a ¼fp i;j g for a i ¼ ; 2; 3; j 2 S i A i and p 2 ¼fp 2;j g for a j 2A 2 [R 2. With this reformuation, we obtain the foowing emma. Lemma 3. (i) (ii) The tota profit of the airine v a ðpþ is jointy concave in p a. The tota profit of the HSR v r ðpþ is jointy concave in p 2;r. Then, the profit functions are concave in the market share (see Appendix for detais). Next, we use the Lambert W function [22] to obtain a cosed-form expression for the market share as foows (see Appendix for detais). Proposition 3. (i) The market share of air transport for cass j 2A i in market i ¼ ; 2; 3 is given by p i;j ¼ W½ P k2a i A i;k Š þ W½ P k2a i A i;k ŠþW½ P A i;j ; k2r i A i;k Š Pk2A i A i;k ð8þ and the market share for HSR for cass j 2R 2 in market i ¼ 2 is given by p 2;j ¼ W½ P k2r 2 A 2;k Š þ W½ P k2a 2 A 2;k ŠþW½ P A 2;j ; k2r 2 A 2;k Š Pk2R 2 A 2;k ð9þ where 23

6 236 K. Sato, Y. Chen A i;j ¼ exp ðb i;j u i;0 b i c i;j Þ : ð0þ (ii) The optima price of air trave for cass j 2A i in market i ¼ ; 2; 3 is given by " fi;j ¼ þ W X #! A i;k þ c i;j : ðþ b i k2a i The optima price of HSR for cass j 2R 2 in market i ¼ 2 is given by " f2;j ¼ þ W X #! A i;k þ c 2;j : ð2þ b 2 k2r 2 From Eqs. () and (2), we note that the optima fare for each sector depends ony on the utiity of a fare casses provided by its own sector and the non-purchase option. In other words, the HSR (or air) price is not affected by the characteristics of the air (or HSR) sector in a competitive market. We aso note that the price difference between the fare casses depends ony on the operating cost, because the first term of Eq. () is the same for each price. However, in practice, fare casses are differentiated by the advance purchase time and other conditions (e.g., canceation and refund poicies), rather than by differences in the operating costs. Thus, the optima price does not fuy express the characteristics of fare cass. The above observations are due to the independence of irreevant aternatives (IIA) property of the mutinomia ogit (MNL) mode. 3 Athough the MNL mode has these drawbacks, it enabes us to obtain the market shares and prices as a simpe cosed-form expression. In the rest of this paper, we focus on the anaysis of the market shares rather than the prices and anayze the competition and cooperation probems when each sector provides a singe fare cass in each market. Thus, we redefine the set of services in each market as foows: N ¼fag, N 2 ¼fa; rg, and N 3 ¼fag. Note that a and r represent the air service and the HSR service, respectivey. Now, we anayze the effect of the service quaity on the market share and optima price. We define the difference between the service quaity and the variabe cost as the cost-adjusted service quaity, ^b i;j b i;j b i c i;j. The costadjusted service quaity ^b i;j aows us to measure the service quaity with consideration of the variabe cost. A high vaue of ^b i;j impies that a firm provides good service for passengers at a ow cost. 3 In fact, some of the iterature takes this into consideration by using a nested ogit mode (e.g., [23 25]). The extension of the demand mode to a nested mode is an interesting and important topic, which we eave for future research. Proposition 3.2 For each market i ¼ ; 2; 3 and sector j 2N i, the market share p i;j and optima price fi;j are increasing in service quaity ^b i;j. In market 2, the market share p 2;j is decreasing with increasing quaity of the competitor s service ^b 2;k, k 6¼ j 2N 2. The interpretation of the mode is mosty intuitive, but we aso provide some further expanation. An increase in the service quaity of the sector in each market increases its market share. As customers vaue service quaity, an increase in service quaity aso impies that they are wiing to pay more, eading to higher optima prices. In addition, this proposition impies that the market share of the air (or HSR) sector decreases as the service quaity provided by the HSR (or air) increases in market 2. Since the air (or HSR) sector does not respond to changes in the riva s service quaity according to the IIA property, its market share decreases with increases in the riva s market share. Reated to this resut, we can aso show the effect of the HSR entities on the air sector share in the HSR-accessibe market (i.e., market 2). From Eq. (8), the air sector share with consideration of the HSR entity is given by p 2;a ¼ W½A 2;a Š=ð þ W½A 2;a ŠþW½A 2;r ŠÞ. When b 2;r!, the air sector share without consideration of the HSR entity can be obtained as p 2;a ¼ W½A 2;aŠ=ð þ W½A 2;a ŠÞ. Thus, the HSR entity has a negative impact on the air sector market share, and the better the service quaity of the HSR is, the more the air sector market share decreases. Simiar resuts have been found in empirica research. Wan et a. [26] used a difference indifference approach and investigated the impact of the commencement of HSR services on airines number of avaiabe seats for domestic fights and the frequency on the affected routes in China, Japan, and South Korea in the samping period They found that China s HSR services with a maximum speed of about 200 km/h (300 km/h) can cause a significant reduction in airine seat capacity on medium-hau (or ong-hau) routes. Since the reduction in avaiabe seats can be considered as a decrease in the market share, their resuts are consistent with our findings. Based on the optima prices and the corresponding market shares, we obtain the maximum tota profits for both sectors. Proposition 3.3 The maximum tota profits of the air and HSR sectors are given by V a ¼ W½A 2;a Šð þ W½A 2;a ŠÞ M W½A ;a ŠþM 2 b b 2 þ W½A 2;a ŠþW½A 2;r Š þ ð3þ M 3 W½A 3;a Š X3 I i;a ; b 3 and i¼ 23 J. Mod. Transport. (208) 26(4):23 254

7 Anaysis of high-speed rai and airine transport cooperation in presence of non-purchase W½A 2;r Šð þ W½A 2;r ŠÞ V r ¼ M 2 b 2 þ W½A 2;a ŠþW½A 2;r Š I 2;r: ð4þ We next derive expressions for the socia surpus by first defining SðfÞ as the consumer surpus from the mutinomia ogit mode (3) and (4). Foowing Sma and Rosen [27], the consumer surpus can be expressed as foows: 0 SðfÞ ¼ X3 M i og@ X e ðb i;j b i f i;jþ þ e ui;0 A: ð5þ b i j2n i i¼ We define the consumer surpus in the competition case as S C Sðf Þ, where f represents the vector of optima prices. The socia wefare is defined as the sum of the tota consumer surpus and tota profits from the air and HSR operators: W C ¼ S C þ V r þ V a : 3.2 Cooperation case ð6þ In the cooperation case, the air and HSR sectors make decisions jointy to maximize their tota profit. The HSR sector not ony operates in market i ¼ 2 (HB) but aso in market i ¼ 3 (AB). Thus, customers who trave from A to B can then choose between air (j ¼ a) and HSR (j ¼ ar) transport for the route HB, N 3 ¼fa; arg. We refer to the air rai service as ar. Thus, in the cooperation case, the HSR (air) is an aternative itinerary for the air (HSR) in market 2. Simiary, the air rai (connecting fights) service can be considered as an aternative itinerary for the connecting fights (air rai) in market 3. The service quaity of the air rai service b 3;ar is affected not ony by the trave time and the frequency for each sector, but aso by the accessibiity between the airport and the HSR station. Customers in market i ¼ face the same decisions as in the competition case. The joint maximization probem of the sectors is given by V ar max v ar ð fþ¼ ~ X3 Xn ~f ~ o i;j d i;j C f ~ i;jð~d i;j Þ ; ð7þ i¼ j2n i where N ¼fag, N 2 ¼fa; rg, N 3 ¼fa; arg and f ~ ¼ ðf ;a ; f 2;a ; f 3;a ; f 2;r ; f 3;ar Þ. The optima price and its expected demand for sector j in market i are denoted by f ~ i;j and ~d i;j ¼ M i ~p i;j, respectivey. We foow the same procedure as in Sect. 3. and prove in Appendix that the profit as a function of the market share is concave. Lemma 3.2 p ar. The tota profit v ar ðp ar Þ is jointy concave in Cosed forms of the optima prices and market shares are aso obtained (see Appendix for detais). Proposition 3.4 (i) The market share of sector j 2N i in markets i ¼ ; 2; 3 is given by P ~p i;j ¼ A P i;j W½ j2n i A i;j Š þ W½ P j2n i A i;j Š ; ð8þ j2n i A i;j where A i;j is given in Eq. (0). (ii) The optima price of sector j 2N i in market i ¼ ; 2; 3 is given by ~f i;j þ W4 X A i;j 5A þ c i;j : b i j2n i ð9þ (iii) The maximum tota profit is given by V ar ¼ X3 < M i W4 X A i;j 5 X = I : i;j b i¼ i ; : ð20þ j2n i j2n i We do not assume that the fare ~f 3;a ( ~f 3;ar ) fufis the non-arbitrage condition; that is, ~f 3;a ( ~f 3;ar ) is ess than or equa to f ~ ;a þ f ~ 2;a ( f ~ ;a þ f ~ 2;r ). In practice, the nonarbitrage condition does not hod in a specific market; that is, an itinerary with a connection at an intermediate city is ess expensive than a ticket from the origin to the intermediate city. This phenomenon is caed hidden-city ticketing. Wang and Ye [28] formuate a fight network revenue management mode to anayze the cause of hidden-city ticketing and its impact on both airines revenues and consumers wefare. They show that the hidden-city opportunity may arise when there is a arge difference in the price easticity of demand for reated itineraries. In our mode, there is a possibiity of this opportunity occurring because the price sensitivity parameter b i, the non-purchase quaity u i;0, and the service quaity b i;j differ from market to market. However, as we show in the next coroary, if the price sensitivity parameter is homogeneous in b i ¼ b for a i ¼ ; 2; 3 and the non-purchase quaity is normaized to zero u i;0 ¼ 0 for a i, then the non-arbitrage condition hods. Coroary 3. Suppose that ¼, b i ¼ b and u i;0 ¼ 0 for i ¼ ; 2; 3. If the operating cost of the connecting itinerary is ower than the sum of the operating cost for the air sector in market and the HSR or air sector in market 2, that is, c 3;a c ;a þ c 2;a (c 3;ar c ;a þ c 2;r ) and the costadjusted service quaity of the connecting fight is ower than the sum of the cost-adjusted service quaity of the air J. Mod. Transport. (208) 26(4):

8 238 K. Sato, Y. Chen sector in markets and 2, that is, ^b3;a ^b ;a þ ^b 2;a, and ^b ;a 2, then we have ~f 3;a ~f ;a þ ~f 2;a ( ~f 3;ar ~f ;a þ ~f 2;r ). This assumption for the operating costs impies that it is too expensive for passengers to purchase air tickets separatey or to switch between modes of transport in terms of the ticketing service fee, connection time, timetabe incompatibiities, baggage transportation, etc. Therefore, in the absence of HSR airine cooperation, it is not worthwhie for any passenger on route AB to use the route AH by air and the route HB by HSR or air. The consumer surpus in the cooperation case is given by S I Sð f ~ Þ, where SðÞ is given in Eq. (5) and f ~ is the vector of the optima prices for the cooperation case. The socia wefare is defined as the sum of the consumer surpus and the tota profit: W I ¼ S I þ V ar : ð2þ 4 Anaysis of the competition and cooperation cases With the cosed-form soutions we derived in Sects. 3. and 3.2, we compare the competition and cooperation cases. First, we investigate the reationship between the market share and optima price between the sectors in a market where the two sectors operate in the same market: market 2 in the competition case and markets 2 and 3 in the cooperation case. Proposition 4. In both the competition and cooperation cases, the cost-adjusted service quaity is positivey associated with the market share in market 2. This is aso appicabe to market 3 in the cooperation case but not the competition case, because the HSR service is not provided in market 3. Finay, in the cooperation case, if the variabe cost c 2;r c 2;a, then the optima price of HSR is ess than that of the air sector in market 2. The air rai itinerary in market 3 is preferabe to air ony, if c 3;ar c 3;a. Furthermore, the difference in the optima price between air and rai in market 2 and air and air rai in market 3 is equa to the difference in the variabe cost between the two sectors. This proposition impies that the reationship between the market shares of both sectors depends not ony on the service quaity but aso on their variabe costs, as the variabe cost affects the optima price. Given that the operating cost of air rai is ower than that of the connecting fights, the practica impication is that enhancing the accessibiity between the airport and HSR station (or b 3;ar increases) coud increase the market share of the air rai itinerary. Finay, since the air rai price is ower than the air price in market 3 in the cooperation case, margina users wi change from air to the air rai itinerary. Next, we formaize the effect of improving the service quaity of the combined air rai transport b 3;ar (e.g., baggage integration, access time to destination, and accessibiity between the airport and HSR station 4 ) on the optima price, market share, tota profit, and consumer surpus in the foowing tabes. Since the fixed and variabe costs, I 3;ar and c 3;ar, are affected by the service quaity, the operator faces a trade-off between the operating cost and service quaity. We assume that the cost-adjusted service quaity of the air rai service is increasing with service quaity, that is, o^b 3;ar =ob 3;ar 0. In other words, the vaue of improving the service quaity exceeds the additiona variabe cost. We focus on market 3, as it is the most reevant. The three choices are isted in the coumns of Tabe 2, and the impacts on their market share, optima price, and tota profit are summarized by the rows. Severa observations can be made from the tabe. First, an increase in the service quaity increases the air rai market share and reduces that of its aternative (connecting fights). This concusion is supported by empirica evidence. For exampe, a surveybased stated preference anaysis by Roman and Martin [30] on passengers at the Madrid Barajas airport showed that one of the main factors for HSR airine cooperation to be successfu is the connection time. Thus, one way to promote air rai options is to increase the number of HSR trains departing from the hub to make the hub more accessibe to fina destinations. This resut aso has an indirect impact on air poution as an increase in the air rai market eads to () the substitution of high-poution air trave with ow-poution HSR and (2) reducing airport congestion, thereby reducing unnecessary fue consumption whie aircrafts wait at runways for takeoff or circing in the air whie waiting for anding (HB). Second, Tabe 2 aso indicates a decine in the probabiity of the nonpurchase option (coumn 3) for market 3 (AB), impying that the tota demand increases with improvement in the service quaity. The increase in trave demand is mosty due to the improvements in the air rai option. As rai infrastructure is aready in pace in most big cities, the IATA [3] suggests that increasing the frequency of trains, and therefore passengers, woud incur itte additiona operating costs. Third, due to the additiona demand (owing to a decine in the non-purchase decision), the prices of both sectors serving market 3 increase. However, consumer surpus aso increases. The decine in consumer surpus for the air rai itinerary due to increased prices coud be more than offset by the increase from improved service quaity, 4 Chiambaretto et a. [29] measure the wiingness to pay of intermoda passengers for some intermoda service attributes using a conjoint anaysis. 23 J. Mod. Transport. (208) 26(4):23 254

9 Anaysis of high-speed rai and airine transport cooperation in presence of non-purchase Tabe 2 Impact of improving the service quaity of air rai on market 3 Market 3 (AB) Connecting fights Air rai Non-purchase Market share # " # Price " " Tota profit Ambiguous Consumer surpus " Socia wefare Ambiguous " Increase, # Decrease, No change eading to a net increase in the consumer surpus. The impact on the tota revenue is not cear. Tota revenue increases when the incrementa revenue is greater than the incurred fixed cost associated with service quaity improvements. Therefore, socia wefare increases with improvement in the service quaity when the increase in the tota profit is reativey arge. These resuts are consistent with Xia and Zhang [32], who aso use a three-node mode to anayze the co-ocation of airports and HSR stations as a form of HSR airine integration and its impact on air and rai operator s profits, consumer surpus, and socia wefare. Xia and Zhang [32] show numericay that both socia wefare and the overa profit of the air and rai operators decrease with the air rai connection time when the margina cost of reducing the air rai connection time is not sufficienty arge. In other words, a reduction in the air rai connection time may improve socia wefare and increase the combined profit. We next turn our attention to the comparison of the impacts on the optima prices and the market share for two cases (competition versus cooperation) in Tabe 3, with each row reporting the impact on each of the three markets. Proposition 4.2 The reationship between the competition and cooperation cases with respect to the optima price and the market share is given in Tabe 3. Since the route AH for market in this instance has the same settings as in the competition case, market is not affected by cooperation. As shown in the second coumn, the optima prices in markets 2 and 3 increase compared to the competition case, mainy because the joint operation of the air and the HSR sectors gives the firms a greater market power. However, even if the airfare or the optima prices increase, the effect of cooperation on the air sector share in market 2 is ambiguous and depends on the comparison of the cost-adjusted service quaity between the air and HSR sectors. We show in Appendix that the conditions under which the air sector market share decreases as a resut of the cooperation, ~p 2;a \p 2;a, incude ) the cost-adjusted J. Mod. Transport. (208) 26(4): Tabe 3 Comparison of optima price and market share between the competition and cooperation cases Market Sector Optima price Market share Tota voume AH (i ¼ ) Air ¼ ¼ ¼ HB (i ¼ 2) Air þ ± - HSR þ ± AB (i ¼ 3) Air þ - þ? Increase by cooperation, - Decrease by cooperation, ± Ambiguous, = Equa/no change service quaity of the air option being ower than that of HSR (^b 2;a ^b 2;r ), and 2) the substitutabiity between the air and the HSR sectors being sufficienty high (i.e., ^b 2;a ^b 2;r ). Thus, when a domestic route is subject to a high eve of competition, that is, (2) hods, cooperation eads to a decrease in passengers to the fina destination B due to a decrease in the air sector market share in market 2. This concusion is supported by some empirica evidences for the reduction in the air sector market share foowing the opening of the air rai service at Frankfurt Airport. During , the numbers of passengers on the routes between Frankfurt and four other major cities, Coogne, Dussedorf, Stuttgart, and Hanover, are reported to have decined by 74.2%, 24.8%, 29.4%, and 23%, respectivey [33]. In addition, as we can see in Tabe 3, the air sector market share in market 3 aso decreases as a resut of cooperation, regardess of the competition eve as measured by the substitutabiity between the air and HSR sectors. This is contrary to the case in market 2 where market shares are affected by the substitutabiity between the two sectors. Therefore, in the panning stage when considering cooperation between the air and HSR sectors, authorities need to carefuy evauate the effect of cooperation on the domestic and connecting air demand to avoid negative consequences for the regiona airports. In terms of the tota voume, Tabe 2 indicates that cooperation eads to a decine in both sectors in market 2, mainy due to the higher prices experienced by the passengers in both sectors. For market 3, whie the air sector market share decreases with cooperation, the tota voume of both itineraries actuay increases, suggesting that the air rai service can increase the size of the market. Thus, cooperation effectivey increases the use of HSR in the domestic market, which is consistent with Jiang and Zhang [3]. Next, we further examine the change in the market share in market 2 for the competition and cooperation cases. Proposition 4.3 If the HSR market share is greater (ess) than the air sector market share in the competition case p 2;r ðþp 2;a, then the HSR share is aso greater (ess) than the air sector share in the cooperation case 23

10 240 K. Sato, Y. Chen ~p 2;r ðþ~p 2;a. In addition, the difference in market share between the HSR and air sectors increases compared to the competition case. In the short medium-distance journey market, the market share of HSR is typicay arger than that of the air sector. An exampe is the market between Tokyo and Osaka, the two argest cities in Japan. The HSR sector is arger than the air sector by a margin of 53% (MLIT [34]). This resut suggests that if the sectors cooperate in such a market, then the HSR share is further increased at the expense of the air sector. Conversey, in a ong-distance journey market, the air sector market share is typicay arger than the HSR share. Proposition 4.3 impies that even if cooperation were to take pace in the ong-distance market, the HSR share woud not ikey increase to a arge extent. Therefore, cooperation shoud be impemented in the short medium-range market to reduce airport congestion. This concusion is supported by empirica evidence. In particuar, anaysis by Givoni and Banister [5] for Heathrow Airport found that HSR airine cooperation for destinations of ess than 600 km is beneficia to airines, passengers, and the environment. Next, we report the resuts of the anaysis of the robustness of cooperation with respect to changes in market conditions. More specificay, we study the reation between the tota market voume and the attractiveness of outside aternatives u i;0, i ¼ ; 2; 3 under changes in market conditions. For both the competition and cooperation cases, we concude that the tota voume for each market is reduced with increasing attractiveness of the no-purchase aternative. However, the decrease in the tota voume for the cooperation case is ower than for the competition case. Proposition 4.4 When the cost-adjusted service quaity of HSR and/or the air sector is greater than that of the nonpurchase quaity, if both sectors cooperate, then the decrease in the tota voume associated with an increase in the non-purchase attractiveness is reduced in market 3. However, this is not the case for market 2. An increase in the attractiveness of the outside option coud aso be due to an increase in the competitors service quaity. One such instance is the entry of ow-cost carriers (LCCs) into the market or a reduction in the to for expressways connecting a hub. In fact, the HSR share for journeys between Kansai (Kyoto, Osaka, and Hyogo) and Fukuoka decreased 2.2% from 20 to 202 after LCCs began operating (MLIT [35]). In such situations, the HSR and air sectors can prevent a arge reduction in their tota market share by cooperating in the connecting market (market 3) because cooperation increases the tota voume in market 3 (Proposition 4.2) by enhancing the service quaity. However, since the tota voume in market 2 decreases the resut of cooperation, cooperation cannot avoid a reduction in profits in this situation. The fina set of resuts focuses on the impact of cooperation on the service providers profit and the consumer surpus. Since the number of potentia customers M i and service quaity ^b i;j differ from market to market, directy comparing the profits and surpuses for a markets for the competition and the cooperation cases might be miseading. We therefore compare these vaues separatey in each of the markets. Let V i and ~V i be the profit in market i for the competition and cooperation cases, respectivey. Note that, by defaut, the profit in market 2 for the competition case is the sum of the profits of the air and HSR sectors: V 2 ¼ V 2;a þ V 2;r. Let S i and W i denote the consumer surpus and socia wefare, respectivey, in market i for the competition case. We use the variabes ~S i and ~W i to represent the consumer surpus and socia wefare in the cooperation case. Proposition 4.5 The reationship between the competition and cooperation cases with respect to the tota profit and consumer surpus for each market is given in Tabe 4. Tabe 4 reports the distribution of socia surpus for the competition and cooperation cases in the three markets, incuding the producers surpus for the air and rai sectors (), consumers surpus (2), and the tota surpus (3), where the number in parentheses corresponds to the coumn number. We discuss each market in a sequence by comparing it to Tabe 3. Because the optima prices and market share in market remained unchanged as reported in Tabe 3, the distribution of the socia, producers (the air and rai sectors) and consumers surpus is equivaent between the two cases. For market 2, together with the ower trave demand (reported in Tabe 3) and higher optima prices, consumers become worse off under the cooperation case. Moreover, the effect on both the market share (Tabe 3), and on the profits earned by the air and rai sectors is uncear. The tota profit in market 2 increases with cooperation ony if the increase in the tota profit resuting from the oss of competition between the HSR Tabe 4 Comparison of tota profit and consumer surpus between the competition and cooperation cases Market Producers profit Consumer surpus Socia surpus () (2) (3) AH (i ¼ ) ¼ ¼ ¼ HB (i ¼ 2) ± - ± AB (i ¼ 3) ± þ ±? Increase by cooperation, - Decrease by cooperation, ± Ambiguous, = Equa/no change 23 J. Mod. Transport. (208) 26(4):23 254

11 Anaysis of high-speed rai and airine transport cooperation in presence of non-purchase and air sectors exceeds the reduction in the tota profit due to the decrease in tota voume under cooperation (see proof of Proposition 4.5(v) in Appendix ). In the next proposition, we further consider the effect of cooperation on the tota profit in market 2. Finay, in market 3, even with higher optima prices, the impact on the consumers is outweighed by the benefit of the increase in trave demand, eading to a higher consumer surpus. A combination of higher optima prices and trave demand resuts in an increase in the producers tota revenue. However, the effect on producers surpus (tota profit) is uncear. If the tota revenue exceeds the fixed cost of air rai transport, then the producer s surpus increases under cooperation. Athough the fixed cost is not considered, this resut agrees with Proposition in Socorro and Viecens [5]. In the above study, when both sectors are assumed to cooperate, the air sector stops operating in market 2 (route HB). That is, the HSR or rai sector operates as a monopoist in the market, and the air and rai jointy earn a higher eve of profit by raising the price of their services. However, in our setting, the air sector continues to provide a service in market 2 even under the cooperation setting. We argue that our resuts and setting are more reaistic, as there is a risk of osing passengers to other airines that operate short-hau fights, as some passengers coud sti prefer to connect to a hub via short-hau fights. This aso refects the operation strategies that many airines use for short-hau fights within routes where they have made intermoda agreements with the HSR sector. For exampe, in the case of Frankfurt Airport, the train service does not fuy repace the air services as exempified by the fact that Lufthansa sti operates air services on the route from Frankfurt to Dussedorf. On the other hand, there is no fight offered by the air sector providing a service between Coogne/Bonn Airport and Frankfurt Airport [36]. Another exampe is the TGV Air service. Despite the services offered by the rai sector, a arge percentage of daiy passenger services and of the tota services run between Paris-CDG and Nantes Airport are sti provided by the air sector (European Regions Airine Association ERAA20). The above exampes support our findings. In addition to the continuation of the service operated by the air sector, we consider the avaiabiity of outside aternatives in each market. Outside aternatives ead to the ambiguity in the resuts for market 2. In the next proposition, we show the effect of outside aternatives in market 2 on the socia surpus in market 2 and for the whoe market. Proposition 4.6 The effect of the service quaity of outside aternatives in market 2 on the socia wefare is summarized in Tabe 5. J. Mod. Transport. (208) 26(4): If the service quaity of the outside options is ow, then customers have itte incentive to choose the outside options. This impies that there wi be imited changes in the tota voume, even if the prices of the services increase under cooperation. Thus, the reduction in the tota profit due to a decrease in the tota market voume under cooperation is ow. In such a case, as in Tabe 4, the producers surpus increases with cooperation because the increase in the tota profit resuting from the remova of competition between the HSR and air sectors exceeds the reduction in the tota profits due to the decreased tota market voume. However, the socia wefare woud aso decrease due to an increase in the consumer surpus. For the specia case in which the non-purchase quaity has a vaue u 2;0 ¼ ^b 2;j ^b 2;j, we can show that the socia wefare in market 2 stricty decreases with cooperation (see the proof of Proposition 4.6(iii) in Appendix ). When the service quaity of the outside aternative is higher than the service quaity of both sectors, cooperation does not impact the consumer surpus, producers surpus, and socia surpus. In a sense, the avaiabiity of outside options upsets the market equiibrium, and the air sector abandons its service entirey. Furthermore, as we reported in Tabe 3, the tota profit in the connecting market (market 3) is increased with cooperation in the case where the fixed cost of the air rai mode is reativey ow. In this case, the tota profit for the whoe market under cooperation is never ower than under competition, and so the airine and the HSR have incentives to cooperate. Proposition 4.7 For ower fixed costs for the air rai mode, if the non-purchase quaity in market 2 is high, then cooperation increases the socia wefare of the whoe market. If not, then cooperation increases the wefare of the whoe market ony in the case where a gain in the wefare in market 3 exceeds a oss in market 2. From this proposition, the fixed cost of the air rai mode and non-purchase quaity in market 2 pay an important roe in determining the effectiveness of cooperation on socia wefare for the whoe market. When the non-purchase quaity in market 2 is high, the effect of cooperation Tabe 5 Reationship between the socia wefare and non-purchase quaity Non-purchase quaity Producer surpus Consumer surpus u 2;0 ^b 2;j þ u 2;0 ^b 2;j Socia wefare? Increase by cooperation, Decrease by cooperation, : Amost equa/no change 23