Access pricing and investment in vertical structures with complementary or rival facilities by Ginés de Rus * M. Pilar Socorro **

Transcription

1 Access pricing nd invesmen in vericl srucures wih complemenry or rivl fciliies by Ginés de Rus M. Pilr Socorro Documeno de Trbjo CÁTEDRA Fede-Aberis Sepember 01 Universidd de Ls Plms de Grn Cnri, Universidd Crlos III de Mdrid y Fundción de Esudios de Economí Aplicd (FEDEA). Universidd de Ls Plms de Grn Cnri y Fundción de Esudios de Economí Aplicd (FEDEA). Los Documenos de Trbjo se disribuyen gruimene ls Universiddes e Insiuciones de Invesigción que lo solicin. No obsne esán disponibles en exo compleo rvés de Inerne: hp:// These Working Pper re disribued free of chrge o Universiy Deprmen nd oher Reserch Cenres. They re lso vilble hrough Inerne: hp:// ISSN: X

2 Access pricing nd invesmen in vericl srucures wih complemenry or rivl fciliies Ginés de Rus,b,c nd M. Pilr Socorro,c,# Universidd de Ls Plms de Grn Cnri. Deprmeno de Análisis Económico Aplicdo, Cmpus de Tfir Ls Plms de Grn Cnri, Spin. b Universidd Crlos III de Mdrid. Deprmeno de Economí Mdrid, Spin c Fundción de Esudios de Economí Aplicd (FEDEA). Jorge Jun 46, 8001 Mdrid, Spin ABSTRACT This pper considers he exisence of given fciliy nd nlyzes he opiml condiions for invesing in complemenry or rivl new fciliy. The fciliies re publicly owned nd re opered by prive firms. Firs, we nlyze he opiml ccess prices o be chrged o prive operors. We find h he opiml ccess price o be chrged for he use of priculr fciliy depends on he degree of complemenriy nd subsiuibiliy beween fciliies. Second, we nlyze under which circumsnces he invesmen in new fciliy is socilly desirble boh in conex wih nd wihou budge consrins. The lernive o be considered if he invesmen is no crried ou necessrily requires opiml pricing. Thus, he invesmen is socilly desirble if here is posiive difference in socil welfre for he cses in which he new fciliy is nd is no consruced nd opiml pricing is pplied. KEYWORDS: invesmen, ccess pricing, vericl srucure, produc differeniion. # Corresponding uhor. Telephone: ; Fx: E-mil ddress: psocorro@de.ulpgc.es. 1

3 1. Inroducion This pper considers he exisence of given fciliy nd nlyzes he opiml condiions for invesing in complemenry or subsiue new fciliy. The indusry is chrcerized by vericl srucure, h is, ech fciliy is owned by firm h provides he infrsrucure o downsrem firms which in urn produce oupu for finl consumers. This is he cse, for exmple, of he rnspor indusry where irpors or ril infrsrucures re used by operors o provide rnspor services o finl consumers. Prive economic goods like hose provided by rnspor operors require specific infrsrucure invesmen. The ownership of key infrsrucure fciliies is commonly public. The sndrd model for he provision of hese goods consiss in he seprion beween ownership (usully public) nd operion (usully provided by prive firms). Someimes he infrsrucure is subjec o inermodl compeiion, like irpors fcing compeiion from high speed ril infrsrucure in medium disnce corridors. In oher cses, he fciliies re considered s complemenry, like he use of he ril infrsrucure o rech irpors. In ll cses ccess pricing for he use of he infrsrucure is criicl. 1 There re some ppers in he lierure nlyzing pricing nd cpciy invesmen in fciliies wih vericl srucure. In priculr, some recen ppers hve pplied his seing in he nlysis of irpors, including he nlysis of non-compeing irpor (Brueckner, 00; Zhng nd Zhng, 006), complemenry irpors (Bsso, 005; Brueckner, 005; Pels nd Verhoef, 004), or n irpor compeing wih oher irpors or rnspor fciliies (Bsso nd Zhng, 007). However, none of hese ppers sudy how ccess pricing is ffeced by he degree of complemenriy or subsiuibiliy beween fciliies, or even more imporn, he condiions under which new complemenry or rivl fciliy should be consruced. 1 Some conrcs leve pricing decisions o he concessionire bu we re ineresed here in he cse where, even wih infrsrucure prive operors, infrsrucure pricing is in he hnd of he regulor. This is he cse of vrible erm concessions where efficien pricing nd profi mximizion wih demnd unceriny is possible hrough he vribiliy of he concession life (see Engel e l., 001)

4 Public invesmens in dediced high speed ril (HSR) infrsrucure h compee direcly wih ir rnspor serves s n excellen cse for he nlysis of ccess pricing, invesmen nd inermodl compeiion. The bse cse is chrcerized by he following: n exising infrsrucure (irpor), public or reguled, is demnded by prively owned commercil irlines opering in open compeiion (inrmodl compeiion) nd noher exising infrsrucure (ril rcks) is provided by monopoly (he ril operor). In his conex, we nlyze he opiml ccess prices o be chrged o prive operors for he use of public infrsrucures in order o mximize he socil welfre of he overll economy in he cse in which here is nd here is no budge consrin. Rel world ccess pricing for he use of priculr public infrsrucure is usully performed by independen gencies h nlyze he specific chrcerisics of such n infrsrucure nd ke pricing decisions in n independen mnner. The Office of Ril Regulion, for exmple, is he independen sfey nd economic regulor for Briin's rilwys nd he Civil Aviion Auhoriy hs s is prime focus o ensure h he irpors Hehrow, Gwick nd Snsed do no exploi heir posiion s monopoly service. There re no inerconnecions beween he decisions of boh gencies. In his pper, we show h if consumers do no consider goods s independen he socilly opiml ccess price for he use of ech public infrsrucure cnno be se in n independen mnner. Moreover, we show h he opiml ccess pricing srongly depends on he budge consrins fced by he regulor. Public infrsrucures involve significn mouns of public funds nd re, essenilly, irreversible so he opiml iming of invesmen is criicl s i is no now or never decision (Dixi nd Pindyck, 1994). To evlue wheher n infrsrucure should or should no be consruced ody we do no only need he projec o hve posiive ne presen vlue compred wih n lernive in which opiml pricing is no pplied, bu lso o increse he socil welfre compred o he siuion in which he infrsrucure is no consruced nd opiml pricing is used. In his sense, if he regulor is no subjec o ny budge consrin we show h he new infrsrucure is more likely o be consruced he higher he prive revenues, he lower he demnd elsiciy nd he lower he socil cos of he invesmen. Given hese vlues, key prmeer is he populion. High individul willingness o py, low opporuniy cos of cpil nd low 3

5 consrucion coss re no enough unless we hve resonble level of demnd, which is proporionl o he number of pssengers. Governmens nd suprnionl gencies rgue h one of he min benefis of ril infrsrucure invesmen is he reducion of environmenl exernliies. In generl, he plne is considered s mode of rnspor more hrmful o he environmen hn he HSR, especilly in regrd o is impc on clime chnge (Euroconrol, 004; Givoni, 007; Schreyer e l., 004). However, we would like o highligh h he environmenl impc of invesmen in HSR poins in wo direcions: one of hem is he reducion in ir nd rod rffic. In such cses is conribuion o reducing he negive exernliies of hese modes could be posiive, hough i requires significn deviion of pssengers from hese modes. Moreover, he use of cpciy mus be high enough o offse he polluion ssocied wih he producion of elecric power consumed by high speed rins (nd in he consrucion period), s well s noise polluion (Kgeson, 009). Ril infrsrucure lso hs negive environmenl impc such s he brrier effec s well s he lnd ken for he ccess rods needed for consrucion nd he subsequen minennce nd operion. The ne blnce of hese effecs depends on he vlue of he ffeced res, he number of people ffeced, he benefi from divered rffic, ec. Given he inense debe in he lierure bou he environmenl coss of ril nd ir rnspor, we hve included such impcs in our model. However, we hve no included oher indirec effecs. The reson is h in undisored compeiive mrkes he ne benefi of mrginl chnge in secondry mrke is zero: no welfre chnges s long s he price chnges re smll. As Greenwld nd Sigliz (1986) poins ou: if firms re mximizing profis nd individuls re mximizing uiliy, boh fcing prices h correcly reflec opporuniy coss, hen sndrd envelope heorem rgumens imply h chnges in profis or uiliy induced by chnges in llocions (resuling from ny smll chnge in prices) re negligible. The res of he pper is orgnized s follows. Secion is dediced o presen he min feures of he model. The model is solved bckwrds. Thus, secion 3 nlyzes he operors mximizion progrms while in secion 4 we discuss he opiml ccess prices. Secion 5 is devoed o nlyze wheher or no new fciliy should be 4

6 consruced by welfre-mximizing regulor nd budge-consrined welfremximizing regulor. Finlly, secion 6 concludes.. The Model Following Dixi (1979) nd Singh nd Vives (1984), we consider n economy composed of n oligopolisic rnspor secor nd compeiive (numerire) secor summrizing he res of he economy. The rnspor secor conins wo public rnspor infrsrucures ( ril infrsrucure nd n irpor) h re used by prive operors. In priculr, he ril infrsrucure is used by prive ril operor while wo prive irlines opere in he irpor. In his conex, benevolen regulor mus decide he ccess prices o be chrged o prive operors for he use of public infrsrucures in order o mximize he socil welfre of he overll economy. Denoe by q 1, q, q he quniy offered by irline 1, irline nd he ril operor, respecively. Consumers re ll idenicl wih uiliy funcion seprble nd liner in he numerire good, m : Uq ( 1, q, q ) m. Therefore, here re no income effecs on he rnspor secor, nd we cn perform pril equilibrium nlysis. Uq (, q, q ) is ssumed o be qudric nd sricly concve: 1 1 U( q1, q, q) uq 1uq uq ( q1 q q qq 1 qq 1 qq ), (1) where u nd u re posiive prmeers, represens he degree of produc differeniion beween irlines, nd represens he degree of produc differeniion beween irlines nd he rilwy. We ssume h pssengers consider h irlines re subsiues bu exhibi brnd loyly o priculr crriers, h is, irlines sell differenied producs. 3 Therefore, rnges from zero when irlines re independen o one when irlines re perfec subsiues (homogenous mrke). On he conrry, pssengers my consider he rilwy nd irlines eiher s subsiues or complemens. Oher rnspor modes cn be included in he numerire secor. 3 Produc differeniion beween irlines my be due o differen resons such s brnd loyly, he exisence of frequen flier progrms, ec. (see, for exmple, Brueckner nd Whlen, 000, or Flores-Fillol nd Moner-Colonques, 007). 5

7 Therefore, we ssume h rnges from minus one when ril nd irlines re considered perfec complemens o one when ril nd irlines re considered perfec subsiues. The prmeer is equl o zero when pssengers consider ril nd irlines s independen goods. However, we ssume h, h is, pssengers consider h one irline cn beer subsiue he oher irline hn he rin. In order o hve he model well defined, we lso ssume h. Pssengers generlized cos is defined s he sum of he icke price, p i wih i 1,,, nd he monery vlue of ime nd/or ny disuiliy componen ssocied wih he specific rnspor mode, nd, which includes ccess, egress, wiing nd in-vehicle ime, discomfor, ec. Thus, he represenive consumer solves: Mx U ( q, q, q ) ( p ) q ( p ) q ( p ) q, () q1, q, q where nd denoe ll coss ssocied wih he specific rnspor mode excep he icke price. The bove mximizion progrm cn be rewrien s: 1 Mx q1q q ( q1 q q qq 1 qq 1 qq ) pq 1 1 pq pq, q1, q, q (3) where nd denoe he mximum (ne of ll excep price) willingness o py for rvelling by ir or by ril, respecively. The uiliy funcion described bove gives rise o liner demnd srucure for he represenive consumer, nd direc demnds cn be wrien s: q b p d p d p, 1 1 q b p d p d p, 1 q b p d p d p 1, (4) where: ( ) (1 ) ( ),, b d 1 (1 )(1 ) (1 )(1 ) (1 ) 1, b,. d

8 We ssume h 0, nd (1 ) 0. Noice h, given our ssumpions,, b, d,, nd b re sricly posiive, while d my be posiive or negive depending on wheher irlines nd he rilwy re subsiues or complemens, respecively. We ssume h when opering irlines nd he ril operor produce n environmenl dmge. Le us denoe by A he environmenl dmge h irlines produce per pssenger nd by T he environmenl dmge per pssenger produced by he ril operor. 4 The iming of he gme is s follows: In he firs period, benevolen regulor mus decide wheher or no o consruc new ril infrsrucure, king ino ccoun h here lredy exiss n irpor nd h consumers perceive he irlines services eiher s subsiues or complemens o he rilwy services. In he second period, he regulor mus decide he ccess price o be chrged o prive operors for he use of public infrsrucures. We disinguish beween welfre-mximizing regulor nd budgeconsrined welfre-mximizing regulor, h is, regulor h mximizes socil welfre bu mus chieve finncil brekeven. In he ls period nd given he ccess prices, prive operors compee in prices wih differenied producs. The gme is solved by bckwrd inducion. 3. Third period: Prive operors mximizion progrms In he hird period, prive operors consider ccess prices s given. Le us denoe by he ccess price chrged o prive irlines for he use of he public irpor, nd by he ccess price chrged o he ril operor for he use of he public ril infrsrucure. Le us denoe by irlines nd ril, respecively. c nd c he consn mrginl opering cos for 4 For he ske of simpliciy, we jus consider opering environmenl coss, ignoring ll fixed environmenl coss h migh rise during he consrucion of he public infrsrucures. 7

9 Ech irline i mximizes is own profis nd, hus, irline i solves he following mximizion progrm: where q i is given by expression (4), wih i 1,. Mx i ( pi c ) qi, (5) The ril operor solves he following mximizion progrm: where q is given by expression (4). pi Mx ( p c ) q, (6) p Firs order condiions for irline 1, irline nd he ril operor s mximizion progrm re given by: 1 p 1 p p b pb p d b c d p 0, 1 b p b pd b c d p 0, 1 b pd p d bc b p 0. 1 (7) Prively opiml icke prices re hen given by: 1 p p ( b d b b bd b c b bcd ) 1 4bb d db 1 p (b d d bd bb dbbcd bbc dbc). 4bb d db (8) Le us now nlyze how opiml icke prices chnge when boh he ccess price for he use of he own public infrsrucure nd he ccess price for he use of he oher public infrsrucure re incresed. Boh resuls re summrized in he following lemms. Lemm 1: The higher he ccess price for he use of he public irpor, he higher he icke price o be chrged o consumers by irlines. The higher he ccess price for he use of he ril infrsrucure, he higher he icke price o be chrged o consumers by he ril operor. Proof: See he Appendix. 8

10 Lemm : If irlines nd he rilwy re subsiues (complemens), he higher he ccess price for he use of he public irpor, he higher (he lower) he icke price o be chrged o consumers by he ril operor. If irlines nd he rilwy re subsiues (complemens), he higher he ccess price for he use of he ril infrsrucure, he higher (he lower) he icke price o be chrged o consumers by irlines. Proof: See he Appendix. 4. Second period: opiml ccess prices In he second period, niciping how prive operors rec o ccess prices, benevolen regulor mus decide he socilly opiml ccess prices o be chrged for he use of public infrsrucures. Le us denoe by C minennce cos of ech public infrsrucure. nd C he mrginl opering nd Willingness o py for cpciy ( WTP cpciy ) per individul is defined s he sum of he individul consumer surplus (CS ), prive operors surplus per individul nd he infrsrucure operor surplus per individul, minus environmenl coss per individul. Formlly: cpciy WTP CS ( C )( q q ) ( C ) q A( q q ) Tq, (9) where CS U ( q1, q, q) ( p1 ) q1 ( p ) q ( p ) q. Thus, willingness o py for cpciy per individul is given by: cpciy 1 WTP q1q q ( q1 q q q1q q1q qq ) ( AC c )( q q ) ( T C c ) q. 1 (10) Suppose h here re N idenicl consumers in he sociey nd h invesmen required o consruc he ril infrsrucure, K denoes he K he invesmen in irpor cpciy nd r is he opporuniy cos of cpil. Then, socil welfre ( SW ) is defined 9

11 s he difference beween he socil willingness o py for cpciy nd he socil cos of cpciy: h is: cpciy SW N WTP rk rk, (11) 1 SW N[ q1q q ( q1 q q q1q q1q qq) ( AC c )( q q ) ( T C c ) q ] rk rk. 1 (1) Noice h shor-run socil mrginl coss for he use of public infrsrucures re given by he sum of he mrginl environmenl cos, he mrginl opering nd minennce cos of he public infrsrucure nd he mrginl opering coss for prive operors, h is: SMC A C c SMC T C c,, (13) where SMC nd SMC denoes he shor-run socil mrginl cos for he use of he irpor nd he shor-run socil mrginl cos for he use of he ril infrsrucure, respecively. We ssume h he mximum (ne of ll excep price) willingness o py for rvelling by ir or by ril is higher hn he shor-run socil mrginl cos for he use of he irpor or he ril infrsrucure, respecively, h is, SMC nd SMC. Moreover, in order o hve he model well defined (posiive quniies) we need o ssume h SMC ( SMC) ( SMC) 1 1. We will consider wo possibiliies: regulor h mximizes socil welfre nd regulor h mximizes socil welfre bu mus chieve finncil brekeven Opiml ccess prices for welfre-mximizing regulor A welfre-mximizing regulor chooses he ccess prices for he use of he irpor nd he ril infrsrucure, nd, in order o mximize he socil welfre given by expression (1). Thus, socilly opiml ccess prices re given by: 10

12 1 AC [ ( SMC ) ( )] SMC 1 1 T C [ ( SMC ) (1 )( SMC )]. 1 (14) Proposiion 1: If consumers do no consider irlines nd ril s independen goods ( 0 ) he socilly opiml ccess price for he use of ech public infrsrucure cnno be se in n independen mnner. The socilly opiml ccess price for he use of priculr infrsrucure is decresing in he mximum willingness o py for rvelling in h rnspor mode nd incresing in he socil mrginl coss of h infrsrucure. However, Proposiion 1 implies h if irlines nd ril re no considered s independen goods he decisions on how much o chrge for he use of priculr infrsrucure mus be ken by considering he willingness o py nd socil coss no only of h priculr good bu lso hose of he oher good. In priculr, if goods re subsiues, he socilly opiml ccess price for he use of priculr infrsrucure is incresing in he mximum willingness o py for rvelling in he oher rnspor mode nd decresing in he socil mrginl coss of he oher infrsrucure. On he conrry, if goods re complemens, he socilly opiml ccess price for he use of priculr infrsrucure is decresing in he mximum willingness o py for rvelling in he oher rnspor mode nd incresing in he socil mrginl coss of he oher infrsrucure. All hese resuls re summrized in he following proposiion. Proposiion : The socilly opiml ccess price for he use of priculr public infrsrucure is higher: he lower is he mximum willingness o py for rvelling in h rnspor mode: / 0, / 0; he higher re he socil mrginl coss of h priculr infrsrucure: / A0, / C 0, / c 0, / T 0, / C 0, / c 0; Moreover, if consumers consider irlines nd ril s subsiues (complemens) he socilly opiml ccess price for he use of priculr public infrsrucure is higher: he higher (lower) is he mximum willingness o py for rvelling in he oher rnspor mode: / ( )0, / ( )0; 11

13 he lower (higher) re he socil mrginl coss of he oher infrsrucure: / T ( )0, / C ( )0, / c ( )0, / A( )0, / C ( )0, / c ( )0. Proof: See he Appendix. Le us look he socilly opiml icke prices nd quniies per individul h re induced by he regulor. Socilly opiml icke prices re obined by subsiuing he socilly opiml ccess prices given by expression (14) ino he prively opiml ickes prices given by expression (8). Proposiion 3: Independenly of he degree of produc subsiuion of irlines ( ) nd he degree of produc subsiuion beween irlines nd he rilwy ( ), socilly opiml ccess prices for welfre-mximizing regulor lwys induce prive operors o chrge icke prices equl o shor-run socil mrginl coss, h is, p p AC c nd p T C c. 1 Proof: See he Appendix. The resul in Proposiion 3 generlizes wh Zhng nd Zhng (006) obined in differen model seing wih homogeneous goods (perfec subsiuion) nd jus one fciliy. Socilly opiml quniies re obined by subsiuing he socilly opiml icke prices given by Proposiion 3 ino he demnd funcions given by expression (4). Thus, socilly opiml quniies for irlines nd he ril operor re given by: 1 q1 q SMC ( SMC) 1 1 q (1 )( SMC) ( SMC) 1 (15) The mximum willingness o py for cpciy per individul cpciy WTP is obined by subsiuing he socilly opiml quniies given by expression (15) ino he funcion given by expression (10). The mximum socil welfre SW is obined by subsiuing 1

14 he socilly opiml quniies given by expression (15) ino he funcion given by expression (1). Tking ino ccoun expressions (14) nd (15), opiml ccess prices cn be rewrien s: 1 AC q1, b (16) 1 T C q. b Proposiion 4: In bsence of environmenl coss, socilly opiml ccess prices for welfre-mximizing regulor re lwys se below he infrsrucure s mrginl opering nd minennce coss. Le us define by 1 he demnd elsiciy of irline 1 or wih respec o his own price evlued in he socil opimum, h is, p. Le us lso denoe by 1 1 b q 1 he demnd elsiciy of he ril operor wih respec o his own price evlued in he p socil opimum, h is,. b Then, opiml ccess prices cn be lso wrien s: q p 1 AC 1 p T C., (17) Proposiion 5: The lower he demnd elsiciy is, he lower is he socilly opiml ccess price for he use of public infrsrucures. The inuiion behind Proposiion 5 is h he higher he monopoly power of prive operors, he lower re ccess prices in order o induce hem o chrge icke price equl o shor-run socil mrginl coss. Moreover, if he demnd elsiciy (in bsolue vlue) is low enough socilly opiml ccess prices my be even negive, h is, he regulor gives subsidies o prive operors in order o induce hem o chrge icke price equl o shor-run socil mrginl coss. The demnd elsiciy (in bsolue vlue) for irlines (rilwy) is higher he higher is b ( b ). 13

15 4.. Access prices for budge-consrined welfre-mximizing regulor In his subsecion we consider benevolen regulor h mximizes socil welfre bu mus gurnee h for ech infrsrucure revenues cover ll coss, including boh opering nd minennce, nd invesmen coss. A regulor h mximizes socil welfre bu mus chieve finncil brekeven solves for ech represenive consumer he following mximizion progrm: 1 Mx SW q1q q ( q1 q q qq 1 qq 1 qq ), ( AC c )( q q ) ( T C c ) q rk rk 1 s.. ( C )( q q ) ( rk ) / N 0, 1 ( C ) q ( rk ) / N 0. (18) If he opiml soluions for welfre-mximizing regulor sisfy he resricions given by expression (18), h is: ( C )( q q ) ( rk )/ N 0, (19) 1 ( C ) ( )/ 0, q rk N (0) hen, he socil opimum for budge-consrined welfre-mximizing regulor is given by expression (17). Therefore, he mximum socil welfre SW obined by welfre-mximizing regulor coincides wih he mximum socil welfre obined by budge-consrined welfre-mximizing regulor. Le us denoe by sw he mximum socil welfre chieved by budge-consrined welfre-mximizing regulor when ny of he condiions given by expression (19) nd (0) is no sisfied. Then, he socil opimum for budge-consrined welfremximizing regulor is obined by solving he mximizion progrm given by (18) nd in he opimum les one of is resricions is binding. Therefore, he mximum socil welfre SW obined by welfre-mximizing regulor is higher hn he mximum socil welfre obined by budge-consrined welfre-mximizing regulor, h is, sw SW. 14

16 5. Firs period: he ril infrsrucure invesmen 5.1. Ril infrsrucure invesmen for welfre-mximizing regulor Suppose s benchmrk he cse in which here is no ril infrsrucure. Then, he represenive consumer s uiliy funcion is given by: 1 Uq ( 1, q) uq 1uq ( q1 q qq 1 ). (1) The represenive consumer mximizes his uiliy minus his generlized cos: Mx U ( q, q ) ( p ) q ( p ) q, () q1, q where denoe he ol ime required o mke rip by ir nd/or ny disuiliy componen ssocied wih he ir rnspor. The bove mximizion progrm cn be rewrien s: 1 Mx q1q ( q1 q qq 1 ) pq 1 1 pq, (3) q1, q where denoes he mximum (ne of ll excep price) willingness o py for rvelling by ir. The uiliy funcion described bove gives rise o liner demnd srucure, nd direc demnds cn be wrien s: (1 ) where 1, b q bp dp 1 1 q bp dp, 1 prmeers, b, nd d re sricly posiive., (4) 1 1 nd d. Noice h given our ssumpions, he 1 In his conex, benevolen regulor mus decide he ccess price o be chrged o prive irlines for he use of he public irpor. Given his ccess price, irlines compee in prices wih differenied producs. In priculr, ech irline i mximizes is own profis nd, hus, irline i solves he following mximizion progrm: Mx i ( pi c ) qi, (5) pi 15

17 where q i is given by expression (4), wih i 1,. Prively opiml icke prices re hen given by: 1 p1 p ( b bc). (6) b d If here is no ril infrsrucure, benevolen regulor chooses he ccess price for he use of he public irpor in order o mximize socil welfre. In his cse, willingness o py for cpciy per individul is defined s he sum of individul consumer surplus, irlines surplus per individul nd public irpor s surplus per individul minus individul environmenl coss. In order words: cpciy 1 WTP q1q ( q1 q q1q ) ( A C c )( q1 q ). (7) Socil welfre is hen defined by: cpciy SW N WTP rk. (8) If here is no ril infrsrucure, welfre-mximizing regulor chooses he ccess price in order o mximize he socil welfre given by expression (8). Thus, he opiml ccess price is given by: A C SMC (1 )( ). (9) In his socil opimum, ickes prices nd quniies re given by: p1 p SMC, 1 q1 q ( SMC ). 1 Thus, if here is no ril infrsrucure he mximum socil welfre h cn be chieved is given by: N SW SMC rk 1 ( ), cpciy 1 where ( ) WTP SMC is he mximum willingness o py for cpciy 1 per individul. (30) (31) Le us now compre he mximum socil welfre h cn be chieved if here is no ril infrsrucure, SW, wih he mximum socil welfre when here is ril operor, 16

18 SW. Le SW infrsrucure nd le SW represen he gin in socil welfre due o he exisence of ril WTP cpciy cpciy WTP denoe he difference in he mximum individul willingness o py for cpciy due o he exisence of ril infrsrucure. Then, he gin in socil welfre due o he exisence of ril infrsrucure is given by: cpciy cpciy SW SW N( WTP WTP ) rk, (3) cpciy cpciy 1 where WTP WTP ( q ). b Denoing by he demnd elsiciy of he ril operor wih respec o his own price evlued in he socil opimum, he difference in he mximum individul willingness o py for cpciy due o he exisence of ril infrsrucure cn be rewrien s: WTP 1 p q. (33) cpciy cpciy WTP Proposiion 6: If he regulor is welfre-mximizer, in he socil opimum he sociey is lwys willing o py more for he exisence of ril infrsrucure. Proposiion 6 ses h, if he regulor is welfre-mximizer, he difference in he mximum individul willingness o py for cpciy due o he exisence of ril infrsrucure is lwys posiive. However, his migh no be enough. In order o consruc ody he ril infrsrucure we need he sociey o be willing o py for he exr coss, h is, we need gin in socil welfre due o he exisence of he ril infrsrucure. Proposiion 7: If he regulor is welfre-mximizer he ril infrsrucure mus be consruced ody if here is gin in socil welfre for he cses in which he new fciliy is nd is no consruced nd opiml pricing is pplied, h is, SW SW 0. In oher words, he ril infrsrucure mus be consruced ody iif nd only if: 1 p q rk. (34) N 17

19 The socil profibiliy of invesing in he new infrsrucure depends on he difference beween he individul willingness o py for cpciy in he cse in which here is ril infrsrucure nd he cse where he ril infrsrucure is no consruced, summrized by he lef hnd side frcion of condiion (34), he cos of he infrsrucure nd he opporuniy cos of cpil. The higher he prive revenues genered by he ril infrsrucure nd he lower he demnd elsiciy of he rin, he more likely is he invesmen o be welfre enhncing. Given hese vlues, key prmeer is he populion (N) served by he new infrsrucure. High individul willingness o py, low opporuniy cos of cpil nd low consrucion coss re no enough unless we hve resonble level of demnd, 5 nd his criiclly depends on geogrphic nd demogrphic condiions. Noice h, in order o be opiml o consruc he ril infrsrucure ody, we no only need o hve posiive socil welfre. Wh we need is he invesmen o be welfre enhncing, h is, induce higher socil welfre hn in he cse in which here is no ril infrsrucure. This is summrized in he following corollry. Corollry 1: A posiive socil welfre for he cse in which ril infrsrucure is consruced, SW 0 is necessry bu no sufficien condiion. The necessry nd sufficien condiion implies posiive difference in socil welfre for he cses in which he ril is nd is no consruced nd opiml pricing is pplied, h is, SW SW 0. All he condiions found in his secion imply he vilbiliy of public funds wihou resricions. In priculr, we hve shown h for welfre-mximizing regulor socilly opiml ccess prices my be se below mrginl opering nd minennce coss. However, he ide of regulor subsidizing prive operors for he use of public infrsrucures my be inccepble, unfesible or even inefficien. Thus, in he nex subsecion we consider benevolen regulor h mximizes socil welfre bu is subjec o cos recovery. 5 From cul consrucion, rolling sock, minennce nd opering coss of Europen HSR lines, verge vlues of ime, resonble rnge of poenil rvel ime svings, nd five per cen discoun re, de Rus nd Nombel (007) find h HSR invesmen is difficul o jusify when he expeced firs yer demnd is below 8 10 million pssengers for line of 500 km, n opiml lengh for HSR o compee wih rod nd ir rnspor. 18

20 5.. Ril infrsrucure invesmen for budge-consrined welfre-mximizing regulor Consider s benchmrk he cse in which here is no ril infrsrucure. If here is no ril infrsrucure, regulor h mximizes socil welfre bu mus chieve finncil brekeven solves he following mximizion progrm: h is:, cpciy Mx SW N WTP rk s.. N[( C )( q q )] rk 0, Mx SW N[ q1q ( q1 q q1q) ( A C c)( q1q)] rk, s.. N[( C )( q q )] rk 0. (35) If he opiml soluions for welfre-mximizing regulor in he benchmrk cse in which here is no ril infrsrucure sisfy he condiion given by expression (35), h is: hen, he mximum socil welfre 1 ( C )( q q ) ( rk )/ N 0, (36) SW obined by welfre-mximizing regulor if here is no ril infrsrucure coincides wih he mximum socil welfre obined by budge-consrined welfre-mximizing regulor if here is no ril infrsrucure. Le us denoe by nd by cpciy wp he mximum willingness o py for cpciy per individul sw he mximum socil welfre chieved by budge-consrined welfremximizing regulor boh if here is no ril infrsrucure nd he condiion given by expression (36) is no sisfied. Then, we cn conclude h wp cpciy cpciy WTP, nd hus, sw SW. Le us now compre he mximum willingness o py for cpciy per individul if here is no ril infrsrucure wih he mximum willingness o py for cpciy per individul when here is ril operor nd he regulor is subjec o cos recovery. We cn disinguish he following cses: 19

21 Cse 1: Condiions (19), (0), nd (36) re sisfied. Then, he difference beween he mximum willingness o py for cpciy per individul when here is ril operor nd he mximum willingness o py for cpciy per individul if here is no ril infrsrucure nd he regulor is subjec o cos recovery is given by: WTP cpciy cpciy WTP 1 p q. Cse : Condiion (36) is sisfied bu condiions (19) nd/or (0) is no sisfied. Then, he difference beween he mximum willingness o py for cpciy per individul when here is ril operor nd he mximum willingness o py for cpciy per individul if here is no ril infrsrucure nd he regulor is subjec o cos recovery is given by: cpciy cpciy cpciy cpciy wp WTP WTP WTP. Cse 3: Condiions (19) nd (0) re sisfied bu condiion (36) is no sisfied. Then, he difference beween he mximum willingness o py for cpciy per individul when here is ril operor nd he mximum willingness o py for cpciy per individul if here is no ril infrsrucure nd he regulor is subjec o cos recovery is cpciy cpciy cpciy cpciy given by: WTP wp WTP WTP 0. Cse 4: Condiion (36) nd les one of he condiions (19) nd (0) re no sisfied. Then, he difference beween he mximum willingness o py for cpciy per individul when here is ril operor nd he mximum willingness o py for cpciy per individul if here is no ril infrsrucure nd he regulor is subjec o cos recovery is given by: wp cpciy wp cpciy. Proposiion 8: If he regulor is budge-consrined welfre-mximizer, in he socil opimum consumers my be willing o py for cpciy less when here exiss ril infrsrucure, h is, wp cpciy cpciy wp 0. Proof: To prove h his possibiliy cn indeed rise, suppose he following couner exmple. Couner exmple: Suppose A 0 nd T = 0 so condiions (19), (0) nd (36) re no sisfied (cse 4) nd in he opimum ll resricions re binding. Suppose he 0

22 following vlues for he prmeers: 0.8, 0.5, 1, 190, c 40, c 0, C 10, C 0, N 50000, ( rk ) / N 000, nd ( rk ) / N 00. The following ble summrizes he resuls: Tble 1: Budge-consrined opiml soluions in Couner exmple Budge-consrined opiml soluions There is ril infrsrucure There is no ril infrsrucure (benchmrk cse) Access prices 135.6, Quniies Willingness o py for cpciy per individul Gin in willingness o py for cpciy per individul due o he exisence of ril Socil welfre sw Gin in socil welfre due o he exisence of ril q1 q , q cpciy wp wp cpciy cpciy q1 q cpciy wp wp sw sw sw This complees he proof. Le us now compre he decision wheher o consruc or no he ril infrsrucure for welfre-mximizing regulor nd budge-consrined welfre-mximizing regulor. In generl, he ril infrsrucure mus be consruced ody if he gin in willingness o py for cpciy for he sociey is higher hn he cos of he invesmen, h is, if here is posiive gin in socil welfre due o he exisence of ril infrsrucure. In order o illusre he differences beween welfre-mximizing regulor nd regulor subjec o cos recovery, le us consider he bove couner exmple. In priculr, le us now compre he budge-consrined opiml resuls in Tble 1 wih he opiml resuls for welfre-mximizing regulor. 1

23 Tble : Opiml soluions for welfre-mximizing regulor in Couner exmple Opiml soluions wihou budge resricions There is ril infrsrucure Access prices 13., There is no ril infrsrucure (benchmrk cse) Quniies q1 q 66.93, q q 1 q 90 Willingness o py for cpciy per individul Gin in willingness o py for cpciy per individul due o he exisence of ril cpciy WTP Socil welfre SW Gin in socil welfre due o he exisence of ril WTP 1707 cpciy SW cpciy cpciy WTP WTP SW SW Compring he resuls in Tble 1 nd Tble we cn conclude h for welfremximizing regulor he ril infrsrucure mus be consruced ody since he gin in socil welfre is higher hn he cos of he invesmen. However, for budgeconsrined welfre-mximizing regulor he exisence of ril infrsrucure implies loss in socil welfre nd i should never be consruced. 6 In generl, we cn disinguish he following cses. Corollry : If condiions (19), (0), nd (36) re sisfied (cse 1), he decision wheher o consruc or no he ril infrsrucure coincides for welfre-mximizing regulor nd for welfre-mximizing regulor subjec o cos recovery. Corollry 3: If condiion (36) is sisfied bu condiions (19) nd/or (0) is no sisfied (cse ), i migh be he cse h welfre-mximizing regulor decides o consruc he ril infrsrucure bu budge-consrined welfre-mximizing regulor does no, h is: sw SW 0 SW SW. Corollry 4: If condiions (19) nd (0) re sisfied bu condiion (36) is no sisfied (cse 3), i migh be he cse h budge-consrined welfre-mximizing regulor 6 Resuls in Tble 1 sugges h under budge consrins, even if we do no ke ino ccoun he cos of he invesmen, he exisence of ril infrsrucure migh be welfre derimenl if fixed nd mrginl minennce coss re oo high.

24 decides o consruc he ril infrsrucure bu welfre-mximizing regulor does no, h is: SW sw 0 SW SW. Corollry 5: If condiion (36) nd les one of he condiions (19) nd (0) re no sisfied (cse 4), i migh be he cse h budge-consrined welfre-mximizing regulor decides o consruc he ril infrsrucure bu welfre-mximizing regulor does no, h is: sw sw 0 SW SW. However, i migh be lso he cse h welfre-mximizing regulor decides o consruc he ril infrsrucure bu budge-consrined welfre-mximizing regulor does no, h is: sw sw 0 SW SW. 6. Conclusions In his pper we nlyze he opiml condiions for invesing in complemenry or subsiue new fciliy. The indusry is chrcerized by vericl srucure, h is, ech fciliy is owned by firm h provides he infrsrucure o downsrem firms which in urn produce oupu for finl consumers. Alhough we use s n exmple he cse of irpors nd ril infrsrucure, we would like o highligh h he min conclusions of he pper regrding ccess prices nd invesmen cn be lso pplied o oher public infrsrucures wih differenied producs considered eiher s subsiues or complemens by consumers. One of he min conclusions of his pper is h he decision on he opiml ccess price o be chrged for he use of priculr infrsrucure mus be ken by considering he exisence of inermodl subsiuions or complemenriies. This resul hs imporn implicion in erms of he insiuionl design of public gencies such s he minisry of rnspor in mny counries, where he division of mngemen unis is usully bsed on echnologicl nd engineering chrcerisics (rod, ir or ril) wih decisions ken in isolion nd wihou considering he overll picure nd he imporn cross-effecs beween differen modes of rnspor. Anoher imporn resul of he pper is reled wih he decision on wheher o consruc or no ody priculr infrsrucure. In his regrd, rdiionl cos-benefi 3

25 nlysis needs o predic icke prices nd quniies. However, ccess prices srongly ffec operors profis nd consumer surplus nd hence icke prices nd quniies. Thus, ccess prices mus be considered in ny cos-benefi nlysis. Moreover, opiml ccess prices vry depending on he resricions fced by he regulor nd hus, such resricions mus be ken ino ccoun in cos-benefi nlysis. In his pper we show h even in he cse in which sociey s willingness o py for he consrucion nd operion of ril infrsrucure is higher hn he invesmen, invesing ody is no necessrily he bes opion. If he bse cse implies no opiml pricing, he posiive ne presen vlue of he invesmen is no sufficien condiion for implemening he projec. The necessry nd sufficien condiion implies posiive difference in socil welfre for he cses in which he new infrsrucure is nd is no consruced, wih opiml pricing being pplied in boh cses. This is no resul derived from he presence of unceriny nd irreversibiliy bu from he inercion of ccess pricing nd invesmen decisions nd he need o consider s benchmrk he cse in which socil welfre is mximized, h is, he cse in which he infrsrucure is no consruced nd opiml pricing is considered. References Bsso, L. J. (005): Airpor ownership: Effecs on pricing nd cpciy. Working Pper, Suder School of Business. The Universiy of Briish Columbi. Bsso, L. J. nd Zhng, A. (007): Congesible fciliy rivlry in vericl srucures. Journl of Urbn Economics 61, Brueckner, J. K. (00): Airpor congesion when crriers hve mrke power. Americn Economic Review 9(5), Brueckner, J. K. (005): Inernlizion of irpor congesion: A nework nlysis. Inernionl Journl of Indusril Orgnizion 3,

26 Brueckner, J. K. nd Whlen, W. T. (000): The price effecs of inernionl irline llinces. Journl of Lw & Economics XLIII, de Rus, G. nd Nombel, G. (007): Is invesmen in high speed ril socilly profible? Journl of Trnspor Economics nd Policy 41, Pr 1, pp. 1 1 Dixi, A. K. (1979): A model of duopoly suggesing heory of enry brriers. Bell Journl of Economics 10, 0-3. Dixi, A.K. nd Pindyck, R. S. (1994): Invesmen under Unceriny. Princeon Universiy Press, Princeon, N.J. Engel, E., Fischer, R. nd Gleovic, A. (001): Les-Presen-Vlue-of-Revenue Aucions nd Highwy Frnchising. Journl of Poliicl Economy 109(5): Euroconrol (004): Anlysis nd modelling of pssenger choice beween ir nd ril rnsporion modes, CARE Innovive Acion Projec, Innovive Roue Chrges Schemes, Work Pckge 3. Flores-Fillol, R. nd Moner-Colonques, R. (007): Sregic Formion of Airline Allinces. Journl of Trnspor Economics nd Policy 41(3), Givoni, M. (007): Environmenl benefis from mode subsiuion: comprison of he environmenl impc from ircrf nd high-speed rin operions. Inernionl Journl of Susinble Trnsporion 1(4), Greenwld, B. C. nd Sigliz, J. E. (1986): Exernliies in economics wih imperfec informion nd incomplee mrkes. The Qurerly Journl of Economics 101(), Kgeson, P. (009): Environmenl specs of iner-ciy pssenger rnspor. OECD- ITF Trnspor Reserch Cenre. Discussion pper,

27 Pels, E. nd Verhoef, E. T. (004): The economics of irpor congesion pricing. Journl of Urbn Economics 55, Schreyer, C., Schneider, C., Mibch, M., Rohenger, W., Doll, C. nd Schmedding, D. (004): Exernl Coss of Trnspor: Upde Sudy. INFRAS nd IWW (Insiu für Wirschfspoliik und Wirschfsforschung, or (rnsled) Insiue for Economic Policy nd Reserch). Singh, N. nd Vives, X. (1984): Price nd quniy compeiion in differenied duopoly. Rnd Journl of Economics 15(4), Zhng, A. nd Zhng, Y. (006): Airpor cpciy nd congesion when crriers hve mrke power. Journl of Urbn Economics 60, Appendix Proof of Lemm 1: We need o check he sign of he following pril derivives: p p b 1 b, d b b d b p 1 d b b b d bb db. We know h b nd b re sricly posiive. Given he definiions of b, d, b, nd d, 1 we hve h: d bb db ( ), which given (1 )(1 ) our ssumpions is clerly negive; 1 (1 )(1 ) bb ( ), db which given our ssumpions is clerly negive. Thus, p 1 0 p nd p 0, s we wned o prove. Proof of Lemm : We need o check he sign of he following pril derivives: p p 1 d 1 b d b b d b, p d b. d b b d b We know h b nd bre sricly posiive while d my be posiive or negive depending on wheher irlines nd he rilwy re subsiues or complemens, 6

28 respecively. Given he definiions of b, d, b, nd d, we hve h: 1 d bb db ( ), (1 )(1 ) which given our ssumpions is clerly negive. Thus, p 1 0 p nd p 0 if irlines nd he rilwy re subsiues, while p 1 0 p nd p 0 if irlines nd he rilwy re complemens. This complees he proof. Proof of Proposiion : We need o check he sign of he following derivives: 1 0; 1 10; 0; A C 1 1 0; 1 c 0; T C 1 0; c 1 ( )0 if ( )0; 1 ( )0 if ( )0; 1 ( )0 if ( )0. A C c 1 1 ( )0 if ( )0; T C c 1 This complees he proof. Proof of Proposiion 3: Subsiuing he socilly opiml ccess prices given by expression (14) ino he opiml icke prices given by expression (8), we ge h p p AC c nd p T C c. This complees he proof. 1 7

29 ÚLTIMOS DOCUMENTOS DE TRABAJO 01-06: Access pricing nd invesmen in vericl srucures wih complemenry or rivl fciliies, Ginés de Rus y M. Pilr Socorro : Trde-offs beween environmenl regulion nd mrke compeiion: irlines, emission rding sysems nd enry deerrence, Crisin Brbo, Ofeli Bencor, M. Pilr Socorro y M. Fernnd Viecens : Lbor Income nd he Design of Deful Porfolios in Mndory Pension Sysems: An Applicion o Chile, A. Sánchez Mrín, S. Jiménez Mrín, D. Roblino y F. Todeschini : Spin 011 Pension Reform, J. Igncio Conde-Ruiz y Clr I. Gonzlez. 01-0: Sudy Time nd Scholrly Achievemen in PISA, Zöe Kuehn y Pedro Lnders : Reforming n Insider-Ousider Lbor Mrke: The Spnish Experience, Smuel Benolil, Jun J. Doldo y Jun F. Jimeno : Infrsrucure invesmen nd incenives wih suprnionl funding, Ginés de Rus y M. Pilr Socorro : The BCA of HSR. Should he Governmen Inves in High Speed Ril Infrsrucure?, Ginés de Rus : L renbilidd privd y fiscl de l educción en Espñ y sus regiones, Angel de l Fuene y Jun Frncisco Jimeno : Trdble Immigrion Quos, Jesús Fernández-Huers Morg y Hillel Rpopor : The Effecs of Employmen Unceriny nd Welh Shocks on he Lbor Supply nd Climing Behvior of Older Americn Workers, Hugo Beníez-Silv, J. Igncio Grcí-Pérez y Sergi Jiménez-Mrín : The Effec of Public Secor Employmen on Women s Lbour Mrke Oucomes, Brindus Anghel, Sr de l Ric y Jun J. Doldo : The peer group effec nd he opimliy properies of hed nd income xes, Frncisco Mrínez-Mor : Public Preferences for Clime Chnge Policies: Evidence from Spin, Michel Hnemnn, Xvier Lbndeir y Mrí L. Loureiro : A Mer of Weigh? Hours of Work of Mrried Men nd Women nd Their Relive Physicl Arciveness, Soni Oreffice y Climen Quinn-Domeque : Mulilerl Resisnce o Migrion, Simone Beroli y Jesús Fernández-Huers Morg : On he Uiliy Represenion of Asymmeric Single-Peked Preferences, Frncisco Mrínez Mor y M. Socorro Puy : Sregic Behviour of Exporing nd Imporing Counries of Non-Renewble Nurl Resource: Txion nd Cpuring Rens, Emilio Cerdá y Xirl López-Oero : Poliicins' Luck of he Drw: Evidence from he Spnish Chrisms Loery, Mnuel F. Bgues y Ber Eseve-Volr : The Effec of Fmily Bckground on Suden Effor, Pedro Lnders : Rndom Wlk Bsed Segregion Mesures, Corlio Blleser y Mrc Vorsz : Incenives, resources nd he orgnizion of he school sysem, Fcundo Albornoz, Smuel Berlinski y Anonio Cbrles : Reiremen incenives, individul heerogeneiy nd lbour rnsiions of employed nd unemployed workers, J. Igncio Grcí Pérez, Sergi Jimenez-Mrín y Alfonso R. Sánchez- Mrín : Socil Securiy nd he job serch behvior of workers pproching reiremen, J. Igncio Grcí Pérez y Alfonso R. Sánchez Mrín : A double smple selecion model for unme needs, forml cre nd informl cregiving hours of dependen people in Spin, Sergi Jiménez-Mrín y Crisin Vilpln Prieo : Helh, disbiliy nd phwys ino reiremen in Spin, Pilr Grcí-Gómez, Sergi Jiménez- Mrín y Judi Vll Cselló : Do we gree? Mesuring he cohesiveness of preferences, Jorge Alclde-Unzu y Mrc Vorsz. 010-: The Weigh of he Crisis: Evidence From Newborns in Argenin, Crlos Bozzoli y Climen Quinn-Domeneque : Exclusive Conen nd he Nex Generion Neworks, Jun José Gnuz nd Mrí Fernnd Viecens : The Deerminns of Success in Primry Educion in Spin, Brindus Anghel y Anonio Cbrles : Explining he fll of he skill wge premium in Spin, Florenino Felgueroso, Mnuel Hidlgo y Sergi Jiménez-Mrín : Some Sudens re Bigger hn Ohers, Some Sudens Peers re Bigger hn Oher Sudens Peers, Toni Mor y Jon Gil : Elecriciy generion cos in isoled sysem: he complemenriies of nurl gs nd renewbles in he Cnry Islnds, Gusvo A. Mrrero y Frncisco Jvier Rmos-Rel.