Subidie for reident paenger in air tranport market Jorge Vaido a,, M. Piar Socorro a,b, Aday Hernández a and Ofeia Betancor a,b a Univeridad de La Pama de Gran Canaria. Departamento de Anáii Económico Apicado, Campu de Tafira. 35017 La Pama de Gran Canaria, Spain b Fundación de Etudio de Economía Apicada (FEDEA). Jorge Juan 46, 28001 Madrid, Spain May 2013 Abtract In ti work, we anaye from a teoretica perpective te efficiency of an ad vaorem and a pecific ubidy for reident paenger in air tranport market. In particuar, we conider paenger wit ig and ow wiingne to pay tat may be reident in a given geograpica area (and terefore entited to a ubidy). A paenger are erved by a monopoy air carrier tat want to get a muc of teir wiingne to pay a poibe. We ow tat if te proportion of reident paenger i ig enoug, nonreident paenger may be expeed from te market. Taken into account ti undeirabe ituation we compare ad vaorem and pecific ubidie. We concude tat if te proportion of paenger wit ig wiingne to pay i ow (ig) enoug appying a pecific (ad vaorem) ubidy for reident paenger i better in ocia term. We appy tee reut to a pecific cae tudy in te Canary Iand were ad vaorem ubidie for reident paenger ave been extenivey ued. We concude tat in mot route te pecific ubidy i undoubtedy better in ocia term. Keyword: reident paenger, pecific ubidy, ad vaorem ubidy JEL Caification: L12, L93, H25 Ti reearc wa undertaken witin te EVA-AIR project, wic i funded by te Spani Minitry of Economic and Competitivene, reearc grant ECO 2012-39277. Te reponibiity for poibe error i oey our. Correponding autor. Te.: +34-928-451836; Fax: +34-928-458183. E-mai addre: jvaido@accione.upgc.e. 1
1. Introduction In Europe air tranport market are uuay free. Any European airine may fy werever it ike witout furter retriction tan te norma requirement regarding te avaiabiity of an operating icence and acce to te airport infratructure deired. Free market are by definition not ubject to reguatory intervention, but ony wen jutified by te exitence of market faiure or for equity reaon. In ti paper we aim to anaye intervention in air tranport market tat take te form of a ubidy on te ticket price. Tee ubidie are an exemption witin te genera European egiation on tate aid rue, aiming to protect paenger from peripera area on a territoria equity bai. 1 It i for exampe te cae of paenger iving in te utraperica region of Canary Iand (Spain); Madeira and Azore (Portuga); Martinique, Reunion Iand, Guadeoupe and Frenc Guyana (France). In a cae te type of ubidie varie from pecific to ad vaorem one, wit ome variant in te adminitrative procedure. Te goa of te intervention i to compenate paenger for te trave cot wen air tranport i an eentia mode of tranport tat ao enure territoria continuity (Cabrera et. a, 2011). In Spain, for exampe, tee ubidie are granted to paenger iving in te arcipeago of te Canarie and Baearic Iand and ao for paenger iving in te Spani autonomou citie of Ceuta and Meia in te nort of Africa wen traveing by air to mainand Spain and in interiand air route. 2 Ti ubidy currenty correpond to 50 percent of te air ticket price. 3 It i wort to mention tat being a ubidy aimed for paenger it i finay paid directy to air carrier on a yeary bai. Mot academic paper concerned wit ubidie in air tranport market focu on te anayi of ubidie in te context of pubic ervice obigation decaration (ee for exampe Reynod-Feigan, 1999; Wiiam, 2005, Wiiam and Pagiari 2004, or Noan et a., 2005). To our knowedge ony Cabrera et a. (2011), Cazada and Fageda 1 Note tat tee ubidie are different tan toe granted to air carrier under a pubic ervice obigation decaration tat are intended to compenate air carrier for te oe incurred during te proviion of decared ervice. 2 Te ubidy i ao granted if paenger trave by boat but in ti paper we focu on air tranport. 3 Atoug tere are ome imitation on te type of fare. For intance buine fare are jut entited to a imited amount of ubidy given by te ubidy tat correpond to te compete economy fare. 2
(2012) and Fageda et a. (2012), attempt to empiricay ae te effectivene of ti type of intervention. Te approac of our paper i teoretica, aiming to anaye te efficiency of ubidie for paenger in it variou form. We are not aware of imiar paper in te ame area, but te iterature about pecific veru ad vaorem taxe/ubidie i extenive. Ad vaorem and pecific taxe are competey equivaent in competitive market, tat i, tey raie te ame revenue and ead to te ame conumer and producer price. However, a firt own by Wicke (1959, originay pubied in 1896) and Suit and Mugrave (1953) ti equivaence doe not appy in a monopoy environment. Severa paper in te iterature ave expored ti non-equivaence between pecific and ad vaorem taxe and ubidie wit imperfect competition. Some paper in te iterature concude tat ad vaorem taxe are better in ocia term tan pecific taxe (ee, for exampe, Suit and Mugrave, 1953 and Skeat and Trande, 1994 (ao extended to oigopoy), for monopoy; Ceung, 1998, or Scröder, 2004, for monopoitic competition; or Deipaa and Keen, 1992, and Denicoò and Matteuzzi, 2000, for oigopoy). However, oter autor ow tat pecific taxe may be more wefare enancing (ee, for exampe, Hamiton, 1999, for monopony; Grazzini, 2006, or Backorby and Murty, 2007, for genera equiibrium; Anderon et a., 2001a, 2001b, Hamiton, 2009, and Wang and Zao, 2009, for differentiated or mutiproduct oigopoie; Pirttiä, 2002, in te preence of externaitie; Kind et a., 2009, in twoided market; or Goerke, 2011, and Kotogianni and Serfe, 2012, under uncertainty). Moreover, wit ubidie te ranking of te two type of intrument may be revered (Coie, 2006; Brander and Spencer, 1984). In ti paper we anaye te efficiency of an ad vaorem and a pecific ubidy for reident paenger in air tranport market. In particuar, we deveop a teoretica mode in wic tere are two type of paenger wit ig and ow wiingne to pay for an air tranport ervice. In addition bot type of paenger may be reident in a given geograpica area and ence, entited to a ubidy, or non-reident. A paenger are erved by a monopoy air carrier tat want to get a muc of teir wiingne to pay a poibe. By doing o it rik eaving out of te market ome type of paenger or eaving oter wit a urpu, wic in turn woud be dependent on te proportion of reident paenger. 3
Ti mode aow u to ow tat te etabiment of paenger ubidie baed on te reidentia condition ead to a reut tat criticay depend on te proportion of reident paenger. In particuar, for a ig enoug proportion of reident paenger, non-reident paenger may be expeed from te market. Taken into account ti undeirabe ituation we compare te poibe effect of bot, an ad vaorem and a pecific ubidy. We concude tat if te proportion of paenger wit ig wiingne to pay i ow (ig) enoug, appying a pecific (ad vaorem) reident ubidy i better in ocia term. Finay, we appy our reut to te cae of te Canary Iand. Even toug ad vaorem ubidie for reident paenger ave been extenivey ued in te Canary route, we can never concude tat ti kind of ubidy i te mot efficient one. In mot route we can undoubtedy tate tat te pecific ubidy woud be ociay better. Te tructure of te paper i te foowing: after ti introduction, ection 2 deveop te mode etup and ection 3 te bencmark cae of no ubidie. Section 4 and 5 expand te framework to incude te anayi of an ad vaorem and a pecific ubidy, repectivey. Bot type of ubidie are compared in ection 6. Our concuion are preented in ection 7. 2. Te teoretica mode We conider an air tranport market operated jut by one airine. Let u denote by N te number of paenger tat may be wiing to fy in ti market. We aume tat tere are ony two type of paenger tat differ in teir wiingne to pay for an air tranport ervice: type paenger, tat i, paenger wit a ig wiingne to pay, and type paenger, tat i, paenger wit a ow wiingne to pay. 4 Hig wiingne to pay paenger are preent in te market in a proportion [0,1]. Neceariy, te proportion of ow wiingne to pay paenger i given by (1 ). Let u denote by H and L te maximum wiingne to pay by type and type paenger, repectivey. By definition, H > L. Bot type of paenger are te ame aircraft cabin and terefore, enjoy te ame quaity of te air ervice (i.e. tere i a inge ca cabin). 4 Hig wiingne to pay paenger may correpond to paenger fying for buine reaon and ow wiingne to pay paenger may correpond to paenger fying for eiure reaon. 4
Te utiitie of bot type of paenger are given by te foowing equation: U H p U L p,, (1) were p and p denote te ticket price carged to type and type paenger, repectivey. Paenger of any type are divided into reident and non-reident in a proportion and (1 ), repectivey, wit 0 1. Reident paenger are entited to a pecia dicount on te ticket price enjoying eiter an ad vaorem ubidy denoted by or a pecific ubidy denoted by S. For te ake of impicity we aume tat te air carrier a a contant margina cot per paenger equa to c. 5 H L c. In order to ave te mode we-defined we aume tat 3. Bencmark cae: No ubidie for reident paenger Te airine cannot perfecty ditingui te type of te paenger and tu, face an advere eection probem. Under perfect information condition, te airine carge a ticket price equa to te maximum wiingne to pay for te air tranport ervice (firtdegree price dicrimination), but wit aymmetric information it need to rey on a econd-degree price dicrimination ytem. Te econd-degree price dicrimination conit of carging different price to different type of paenger. To do o, te airine need to induce ef-eection. In particuar, in order to induce paenger to revea teir rea type, te airine offer retricted and non-retricted ticket. Retricted ticket are ceaper ( p ) tan nonretricted ticket ( p ), but tey are ubject to a et of imitation tat make paenger to incur in an additiona cot (for exampe, tey are non refundabe ticket needed to be bougt ome day in advance, no cange are aowed, a Saturday tay i required, etc.). 5 Te iterature on tranport cot function i quite extenive. In particuar, Oum and Water (1997) find many exampe of contant return to cae for te air tranport indutry in te cae of airine (even out of ten tudie). 5
Let u denote by c and c te additiona cot faced by type and type paenger if tey acquire a retricted ticket, wit c c. For te ake of impicity and witout o of generaity, we normaize c 0. Moreover, we aume tat H L c. Te efeection or incentive compatibiity contraint are given by: H p H p c L p L p., (2) So te airine induce ef-eection by carging te foowing price for retricted and non-retricted ticket: p 0 L, p p c L c 0 0, (3) were te ubcript 0 refer to te bencmark ituation in wic tere i no ubidy. Lemma 1: If tere are no ubidie for reident paenger, type paenger are away carged teir maximum wiingne to pay. On te contrary, type paenger are carged a iger price tan type paenger, keeping a conumer urpu equa to H L c. Te optima profit for te airine in te bencmark ituation are given by te foowing expreion: 0 N L c 1 NL Nc. (4) 4. An ad vaorem ubidy for reident paenger Let u conider now te cae in wic te government ubidize air trave for reident paenger. Ti ubidy take an ad vaorem form, tat i, it i etabied a a percentage of dicount on te ticket price and it i equa to, wit (0,1). Let u denote by k p d te fina price paid by a type k paenger, and by k p te price carged by te airine to a type k paenger, wit k,. If te type k paenger i non-reident, no 6
k k ubidy i appied and p p. On te contrary, if te type k paenger i reident, e d k k enjoy an ad vaorem ubidy and pay a ticket price p p (1 ). In ti context, te airine need to decide te bet pricing trategy and we can ditingui four aternative pricing trategie. d Strategy 1: Set p L/ (1 ) and p L c. Strategy 1 impie carging type reident paenger a ticket price equa to teir maximum wiingne to pay increaed by te amount of te ubidy. Ti eave out of te market type non-reident paenger. On te contrary, type paenger are carged te ame price a in te ituation witout ubidie. Tu, a type paenger buy te air tranport ticket and type reident paenger are eft wit an additiona urpu given by te amount of te ubidy. Strategy 2: Set p L/ (1 ) and p ( L c ) / (1 ). Strategy 2 impie carging to type and type reident paenger a ticket price equa to teir maximum wiingne to pay increaed by te amount of te ubidy. Ti eave out of te market type and type non-reident paenger. Strategy 3: Set p L and p ( L c ). Strategy 3 impie carging bot type and type paenger te ame ticket price a in te ituation witout ubidie. Tu, a paenger buy te air tranport ticket and bot type and type reident paenger are eft wit an additiona urpu given by te amount of te ubidy. Strategy 4: Set p L and p ( L c ) / (1 ). Strategy 4 impie carging type reident paenger te ame price a in te ituation witout ubidie. Tu, a type paenger buy te air tranport ticket and type 7
reident paenger are eft wit an additiona urpu given by te amount of te ubidy. On te contrary, type reident paenger are carged a ticket price equa to teir maximum wiingne to pay increaed by te amount of te ubidy. Ti eave out of te market type non-reident paenger. Notice tat eac trategy impie a trade-off between increaing te ticket price and oing te non-reident paenger demand. Let u denote by i te airine profit obtained by appying trategy i wen an ad vaorem ubidy for reident paenger i introduced. Te airine profit for eac trategy are ten given by te foowing expreion: L 1 N ( L c ) (1 ) (1 ) Nc. 1 L c L 2 N (1 ) (1 ) Nc. 1 1 (5) (6) 3 N ( L c ) (1 ) L Nc. (7) L c 4 N (1 ) L (1 ) Nc. 1 (8) In order to find te optima trategy we need to compare te profit given by expreion (5), (6), (7), and (8). Te optima pricing deciion, a we wi ow, i conditiona on te reident proportion δ. We tart by comparing profit by pair. Ti comparion give u te critica vaue of ij tat make bot profit equa, wit i, j 1,...,4 and i j.6 Afterward, we anayze wic trategy i dominant and te condition for tat to appen. Propoition 1: If 0 13 24 trategy 3 i tricty dominant. However, for intermediate vaue of ( 13 24 21 43 ), trategy 1 i tricty dominant. Finay, if 21 43 1, trategy 2 tricty dominate. 6 Te order of te ub-index indicate tat, for vaue of δ greater tan te critica vaue profit aociated wit trategy i i greater tan te profit aociated wit trategy j. 8 ij, te airine
Proof: In order to know wic profit i preferred, we compare trategie two by two, obtaining ix critica vaue of, tat i, 21, 13, 14, 23, 24, and 43. Starting ij wit trategy 1 and trategy 2, we obtain te critica vaue. Foowing te ame 21 procedure for trategy 3 and trategy 4 we get te critica vaue. 43 We are ao intereted in knowing ow profit beave wen ij i different from te critica vaue. To do tat we need to compute te partia derivative of te previou comparion of profit wit repect to. Formay: L c c (1 ) 1 2 3 4 0 21 43. L c(1 ) c ( 1 2 ) ( ) 3 4 0 for a, (0,1). We oberve tat 21 43. Moreover, for 21 43, 1 2 and 3 4, repectivey. Simiary, we get 13 24 and 1 3 and 2 4 for 13 24. Lc (1 ) 1 3 2 4 0 13 24. Lc(1 ) ( 1 3 ) ( 2 4 ) 0 for a, (0,1). Moreover, 23 and 2 3 for 23. Formay: L c c (1 ) 2 3 0 23. L c(1 ) c ( 2 3 ) 0 for a, (0,1). Finay, we ao obtain te critica vaue of 14 by comparing profit from trategy 1 and trategy 4. To know ow profit beave for vaue of different from ti critica vaue, we need an extra condition depending on te proportion of type and type paenger. Formay: 9
(1 ) ( L c)(1 2 ) c 1 4 0 14. (1 2 )( L c(1 )) c ( 1 4 ) Lc(1 ) 0 if. 2( L c(1 )) c ( 1 4 ) Lc(1 ) 0 if. 2( L c(1 )) c Terefore, for any * 14, 1 4 if and 4 1 if *, wit * Lc(1 ). 2( L c(1 )) c Conequenty, ranking te critica vaue we wi obtain te foowing condition: ij * If 0, 14 13 24 23 21 43. * If 1, 13 24 23 21 43 14. We concude tat if 0 13 24, trategy 3 i tricty dominant. However, for intermediate vaue of ( 13 24 21 43 ), trategy 1 i tricty dominant. Finay, if 21 43 1, trategy 2 tricty dominate. Ti compete te proof. In order to determine wic trategy dominate we can ditingui ten different area (ee Figure 1) in te pace (, ). In region I, II and III, trategy 3 i preferred. In region IV, V, VI and VII trategy 1 i dominant, wie in region VIII, IX and X, trategy 2 i te preferred one. Finay, trategy 4 i tricty dominated for every (0,1). 10
Figure 1. Dominant trategie for different region wit an ad vaorem ubidy for reident paenger 14 1 1 IV I VIII V II IX VI III X VII 23 21 43 13 24 * 1 α 14 Te depicted area ow wat trategie are preferred. Te adow area repreent te pace were trategy 3 i dominant, te wite one repreent te pace for trategy 1 and te triped area indicate were trategy 2 dominate. From Propoition 1 and Figure 1, it i oberved tat te critica vaue 14 and 23 irreevant in te anayi. Ti mean tat optima trategie are independent of te are vaue of ( 14 and 23 are te ony critica vaue tat depend on and tey do not pay any roe in te previou anayi). Coroary 1: Te airine cooe a trategy independenty of te proportion of type and type paenger,. Type paenger pay a iger price tan type paenger. Te airine take into account ti difference in price and never cooe a trategy uc tat type nonreident paenger are expeed from te market and type non-reident paenger are not. In oter word, if te airine doe not provide ervice for type non-reident 11
paenger, neiter doe it for type non-reident paenger. Tu, for every (0,1), trategy 4 i never optima. Ti i formay tated in te foowing propoition. Propoition 2: If (0,1) trategy 4 i never tricty dominant. In te extreme cae were a paenger ave a ig wiingne to pay, tat i 1, or a ow wiingne to pay, tat i 0, trategy 4 coincide wit trategy 2 or trategy 3, repectivey, and tu it may be coen. Proof: On te one and, if 0 we can ee tat 3 i equa to 4, tat i, trategy 3 and trategy 4 are equivaent. In addition 1 and 2 are ao identica wat impie tat trategy 1 and trategy 2 are ao equivaent. On te oter and, if 1 1 equa to 3, and 2 i equa to 4. Ti mean tat trategy 1 and trategy 3 are equivaent and trategy 2 and trategy 4 are equivaent too. Formay: - If 0 and: 0, trategy 3 and trategy 4 are tricty 14 24 13 23 dominant., a trategie are equivaent. 14 24 13 23 14 24 13 23 1, trategy 1 and trategy 2 are tricty dominant. i - If 1 and: 0, trategy 1 and trategy 3 are tricty 14 12 34 23 dominant., a trategie are equivaent. 14 12 34 23 14 12 34 23 1, trategy 2 and trategy 4 are tricty dominant. Ti compete te proof. 12
Figure 2 repicate te reut in Figure 1, igigting te tree reevant region. Region A repreent te pace were trategy 3 i dominant, region B repreent te pace for trategy 1 and region C indicate te region were trategy 2 dominate. Figure 2. Dominant trategie for different vaue of (, ) wit an ad vaorem ubidy for reident paenger 21 43 1 C 13 24 B A 1 α Coroary 2: Depending on te vaue of (proportion of reident paenger), wen an ad vaorem ubidy for reident paenger i introduced we wi end up in one of te foowing region: Region A: correpond to a ituation in wic ticket price remain a in te ituation witout ubidie. Region B: correpond to a ituation in wic te ticket price for type paenger i increaed by te amount of te ubidy and type paenger are carged te ame price a in te ituation witout ubidie. Ti eave out of te market type non-reident paenger. Region C: correpond to a ituation in wic a ticket price are increaed by te amount of te ubidy. Ti eave out of te market a non-reident paenger. 13
Te aim of air tranport ubidie for reident paenger i to protect paenger from peripera area on a territoria equity bai. Tu, te purpoe of te reguator i to guarantee tat te ubidy doe not affect te fina price carged by te airine, aowing reident paenger to enjoy te woe ubidy and pay ceaper ticket but witout affecting te ticket price carged to non-reident paenger. Tu, region A repreent te mot deirabe ituation, ince ticket price remain a in te ituation witout ubidie. Foowing te ame reaoning, region C repreent te e deirabe ituation in wic te airine capture a reident paenger urpu and non-reident paenger are driven out of te market. Ti i formay tated in te foowing coroary. Coroary 3: Wen an ad vaorem ubidy for reident paenger i introduced, region A correpond to te mot deirabe ituation and region C correpond to te wort ituation in ocia term. 5. A pecific ubidy for reident paenger Let u conider now tat te government grant a pecific ubidy intead of an ad vaorem one. Tu, te government pay a fixed amount of money for eac air tranport ticket bougt by a reident paenger, independenty of te ticket price. Reca tat k p d denote te fina price paid by a type k paenger, and k p te price carged by te airine to a type k paenger, wit k,. If te type k paenger i non-reident, no k k ubidy i appied and p p. On te contrary, if te type k paenger i reident, e d k k enjoy a pecific ubidy and pay a ticket price p p S. Again, te airine need to decide it bet trategy in pricing term. Te airine a four different price poibiitie to conider: d Strategy 1 : Set p L S and p L c. Strategy 2 : Set p L S and p L c S. 14
Strategy 3 : Set p L and p L c. Strategy 4 : Set p L and p L c S. Te intuition beind trategie 1, 2, 3 and 4 are imiar to toe aready expained in te previou ection for trategie 1, 2, 3 and 4. Let u denote by i S te airine profit obtained by appying trategy i wen a pecific ubidy for reident paenger i introduced. Te airine profit function for eac trategy are given by: S 1 N ( L c ) (1 ) ( L S) (1 ) Nc. (9) S 2 N ( L c S) (1 )( L S) (1 ) Nc. (10) S 3 N ( L c ) (1 ) L Nc. (11) S 4 N ( L c S) (1 ) L (1 ) Nc. (12) We foow te ame procedure a in te previou ection. Terefore we compare profit by pair in order to obtain te critica vaue of S ij. Ti aow u to find wic trategy i dominant and under wat condition ti dominance take pace. Propoition 3: If 0 S S 13 24 trategy 3 i tricty dominant. However, for S S S intermediate vaue of ( 13 24 21 S 43 ), trategy 1 i tricty dominant. S S Finay, if 21 43 1, trategy 2 tricty dominate. Proof: Te proof of ti propoition i imiar to te one of Propoition 1 15
Propoition 4: If (0,1) trategy 4 i never a tricty dominant trategy. In te extreme cae were a paenger ave a ig wiingne to pay, tat i 1, or a ow wiingne to pay, tat i 0, trategy 4 coincide wit trategy 2 or trategy 3, repectivey, and tu it may be coen. Proof: Te proof of ti propoition i imiar to te one of Propoition 2 Our ranking between profit and trategie do not vary wit repect to te previou ection. Tat i, our reut are quaitativey identica but te magnitude and te critica vaue are numericay different. We iutrate te ituation now in Figure 3. Figure 3. Dominant trategie for different vaue of (, ) for reident paenger wit a pecific ubidy S S 21 43 1 C S S 13 24 B A 1 α Simiary to Figure 2, we ave tat in region A trategy 3 i tricty dominant (a paenger are erved); in region B trategy 1 i tricty dominant (ony type reident paenger and a type paenger are erved); wie in region C trategy 2 i tricty dominant (ony reident paenger are erved). 16
Coroary 4: Depending on te vaue of (proportion of reident paenger), wen a pecific ubidy for reident paenger i introduced we wi end up in one of te foowing region: Region A : correpond to a ituation in wic ticket price remain a in te ituation witout ubidie. Region B : correpond to a ituation in wic te ticket price for type paenger i increaed by te amount of te ubidy and type paenger are carged te ame price a in te ituation witout ubidie. Ti eave out of te market type non-reident paenger. Region C : correpond to a ituation in wic a ticket price are increaed by te amount of te ubidy. Ti eave out of te market a non-reident paenger. Once again, region A correpond to a ituation in wic price remain a in te cae witout ubidie. Ti i te bet ituation in ocia termte ubidy benefit te reident paenger and non-reident paenger are unatered. On te contrary, region C correpond to a ituation in wic a price are increaed and a non-reident paenger are expeed from te market. Ti atter ituation i te wort ituation in ocia term. Ti i formay tated in te foowing coroary. Coroary 5: Wen a pecific ubidy for reident paenger i introduced, region A i te mot deirabe ituation and region C i te wort ituation in ocia term. 6. Comparion between ad vaorem and pecific ubidie for reident paenger 6.1. Ad vaorem v. pecific ubidie: te critica vaue In ti ubection we compare te two propoed ubidy mecanim and we ow under wat condition one i preferred to te oter. To approac ti probem, we compare te depicted area of Figure 2 and 3, taking into account tat te greater region A and A and/or te ower region C and C are, te better in ocia term. Let u conider te ame pubic expenditure for a pecific and an ad vaorem ubidy for reident paenger, tat i, S (1 ) L ( L c ). Wit uc a pecific ubidy, 17
type (type ) reident paenger are receiving a iger (ower) ubidy tan te one obtained wit an ad vaorem ubidy, L S ( L c ). Keeping contant te government expenditure, a pecific ubidy woud be ociay preferred to an ad vaorem ubidy if region A i greater or equa tan region A and/or region C i maer or equa tan region C. Ti comparion trongy depend on, tat i, on te proportion of ig wiingne to pay paenger. Propoition 5: Tere i a critica treod ( L) / ( c (1 )) uc tat, for every, if, a pecific ubidy for reident paenger i ociay preferred to an ad vaorem one. Proof: We can obtain te condition tat make region A greater or equa tan region A. AD S L By oving 13 13 we get tat S. Ti pecific ubidy ao impie tat 1 AD ( L c ) region C i ower tan C ( 12 S 12 ), ince ti od if S. 1 L Since S (1 ) L ( L c ), we need (1 ) L ( L c ), tat i, 1 ( L) / ( c (1 )). Ti compete te proof. Propoition 5 tate tat if te proportion of ig wiingne to pay paenger in te market i ow enoug, for a given pubic expenditure, a pecific ubidy for reident paenger i ociay better tan an ad vaorem one. Propoition 6: Tere i a critica treod ( L c ) / ( c (1 )) uc tat, for every, if an ad vaorem ubidy for reident paenger i ociay preferred to a pecific one. 18
Proof: We can obtain te condition tat make region C greater or equa tan region C. By oving AD 12 S we get tat ( L c ) 12 S. Ti pecific ubidy ao impie tat 1 AD L region A i ower tan region A ( 13 S 13 ), ince ti od if S. 1 Since S (1 ) L ( L c ), we need ( L c ) (1 ) L ( L c ), 1 tat i, ( L c ) / ( c (1 )). Ti compete te proof. Propoition 6 tate tat if te proportion of ig wiingne to pay paenger in te market i ig enoug, for a given pubic expenditure, by appying an ad vaorem ubidy for reident paenger te ociety i more ikey to end up in te mot deirabe ituation, and e ikey to end up in te wort ituation. Tu, an ad vaorem ubidy for reident paenger i better from a ocia point of view tan a pecific one. Notice tat for intermediate vaue of we cannot undoubtedy concude wic ubidizing ytem i better in ocia term. Te reaon i tat for intermediate vaue of region A may be greater tan region A, but ao region C may be greater tan region C and ence, te optimaity of one poicy over te oter depend on, tat i, on te pecific region tat we are conidering. Finay, we woud ike to igigt tat, toug te vaue of mut beong to te coe interva [0,1], te critica vaue of and are away poitive but not neceariy ower tan one. Tu, if 1 every wi be ower or equa tan and a pecific ubidy for reident paenger wi be away ociay better tan an ad vaorem one. Ti i formay tated in te foowing coroary. Coroary 6: If 1 a pecific ubidy for reident paenger i away ociay preferred to an ad vaorem one. In ummary, if i ower tan or equa to, a pecific ubidy for reident paenger i ociay better. In contrat, if i greater tan or equa to, an ad vaorem ubidy 19
for reident paenger i preferred. Finay, for intermediate vaue of we cannot undoubtedy concude anyting about te optima poicy. We can ummarie tee reut in Figure 4. Figure 4. Critica vaue of α 0? Specific Ad vaorem Notice tat bot treod, and, depend on te ow and ig wiingne to pay paenger ticket price in te abence of ubidie ( p0 L and p0 L c ) and on te inconvenience cot faced by type paenger wen buying a retricted-ticket. Bot treod are tricty increaing in and te ticket price. However, te ower te difference between te retricted and non-retricted ticket price, te greater te vaue of tee treod. Notice tat on te one and, for a given, te ower te difference between te retricted and non-retricted ticket price i, tat i te ower c i, te more ikey i to tay in te area in wic te pecific ubidy i preferred and, te e ikey i to tay in te area in wic te ad vaorem ubidy i preferred. On te oter and, for a given c, te ower i te more ikey i to tay in te area in wic te pecific ubidy i preferred. In oter word, te coer i te pecific ubidy S to te vaue L (te ad vaorem ubidy for type paenger), te more ikey i tat te pecific ubidy dominate te ad vaorem one. c 6.2. An empirica appication: Te cae of te Canary Iand In order to iutrate te reevance of our teoretica finding we make ue of te cae of interiand air tranport in te Canary Iand. Hence, we proceed by etimating wit 20
rea data te critica vaue of tat make one type of ubidy ociay preferred to te oter for te ame government expenditure. Our teoretica mode fit quite we witin te current ituation of interiand air tranport in te Canary Iand. At te moment tere i jut one air carrier (Binter Canaria) tat provide tee ervice. Te type of aircraft fown i unique (ATR 72-500) and a paenger are te ame cabin ca. In addition, te pricing tructure i pretty impe wat faciitate our etimation of critica vaue of. At te moment paenger wit reidence in te iand are entited to a 50 per cent ubidy on te ticket price. Nevertee ti ubidy a evoved aong time, ince a 10 per cent (in appication from 1987 to 1998), to a 33 per cent (in appication from 1998 to 2004), to a 38 per cent (in appication from February to December 2005), to a 45 per cent (in appication in 2006), and to te current 50 per cent (in appication from 2007 to nowaday). In order to enjoy te ubidy paenger need to faciitate te reevant data to te airine, wic in turn, wi get te money correponding to ti ubidy directy from te government on a yeary bai. At te moment ti iue i under review, and we woud expect a cange in te ceme in te coming future. In order to ceck te poibe vaue of te treod we ave cacuated tem for te cae of ome interregiona figt between iand. We eect te main route in term of number of paenger (See Tabe 2). Source: AENA. Tabe 2. Main inter iand route in te Canary Iand Route Paenger (2011) Tenerife Nort - Gran Canaria 698.457 Tenerife Nort - La Pama 616.552 Gran Canaria - Fuerteventura 599.049 Gran Canaria - Lanzarote 590.899 Tenerife Nort - Lanzarote 286.454 Tenerife Nort - Fuerteventura 193.789 Tenerife Nort - E Hierro 139.536 Gran Canaria - La Pama 115.074 21
Price data are taken from te company webite for a one way ticket wit two mont in advance of te figt. We conider tat te vaue for c i given by te difference between te ceapet and te more expenive ticket. We ao need to take into account * tat 0.5. repreent te vaue of for wic 1, and ence te ad vaorem ubidy for reident paenger may be ociay better tan a pecific ubidy. Te reut are preented in Tabe 3. Tabe 3. Treod vaue for main inter iand route in te Canary Iand p0 L p0 L c c * Tenerife Nort - Gran Canaria 41 77 36 1,14 2,14 0,32 Tenerife Nort - La Pama 41 81 40 1,03 2,03 0,33 Gran Canaria - Fuerteventura 43 87 44 0,98 1,98 0,34 Gran Canaria - Lanzarote 50 100 50 1,00 2,00 0,33 Tenerife Nort - Lanzarote 60 130 70 0,86 1,86 0,35 Tenerife Nort - Fuerteventura 61 123 62 0,97 1,97 0,34 Tenerife Nort - E Hierro 48 87 39 1,23 2,23 0,31 Gran Canaria - La Pama 58 122 64 0,91 1,91 0,34 Note: Price are in euro for a one way ticket. Data wa coected on te 2 nd of November 2012. We can ee tat in mot route te vaue of i greater tan one. Tu in toe route, for any vaue of, a pecific ubidy for reident paenger i ociay preferred. Moreover, in a te route for wic te vaue of i ower tan one, i around two. Tu, we can never concude tat te ad vaorem ubidy i te preferred one. We can compute te vaue of tat make 1, tat i, *. We find tat for any iger or equa tan 33 per cent on average an ad vaorem ubidy for reident paenger (wic i indeed te poicy tat a been appied in te Canary Iand ince 2001) i never ociay preferred to a pecific ubidy. For ower tan 33 per cent on average, te ad vaorem ubidy wi be ony ociay better tan a pecific ubidy if te proportion of ig wiingne to pay paenger,, i ig enoug. 22
7. Concuion In ti work we ave deveoped a teoretica mode tat aim to anaye te efficiency of paenger ubidie in European air tranport market. Tee ubidie are not frequent, and wen appied tey are intended to protect te interet of paenger from outermot region witin te EU, being baed on a reidentia feature. Our mode ditinguie between two type of paenger: paenger wit a ig and wit a ow wiingne to pay. Te proportion of bot type of paenger and te proportion of reident paenger in eac group appear to be paying a very important roe in te market. On te one and, depending on te proportion of reident paenger, it may even appen tat non-reident paenger woud be expeed from te market. If te objective of te poicy i te protection of peripera reident paenger witout damaging te interet of non-reident paenger, ti i an undeirabe equiibrium. On te oter and, we ave ao compared our reut for two variant of ubidie: an ad vaorem and a pecific one. In bot cae te danger of eaving non-reident paenger out of te market arie. In turn, bot type of ubide woud be more or e damaging for non-reident paenger depending on te proportion of ig and ow wiingne to pay paenger. We ue te Canary Iand cae in order to iutrate ow our finding can be empiricay appied. We find tat for tee route we can never concude tat te ad vaorem ubidy i te preferred one. Finay, we woud ike to igigt tat in ti paper we are not jutifying te ue of ubidie for reident paenger but ony dicuing teir poibe effect and te bet way of appying uc ubidie (eiter wit an ad vaorem or a pecific ubidy). It remain to be own weter a paenger ubidy baed on oter criteria (e.g. route criterion) oud be ociay better tan ubidie for reident paenger. Ti i an iue tat deerve anoter reearc. 8. Reference Anderon S.P., A. de Pama, and B. Kreider (2001a): Te efficiency of indirect taxe under imperfect competition. Journa of Pubic Economic, 81(2): 231 251. Anderon, S.P, A. de Pama, and B. Kreider (2001b): Tax incidence in differentiated product oigopoy. Journa of Pubic Economic, 81 (2), 173-192. 23
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