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Airport complementarity: Private vs. government ownership and welfare gravitation
Transportation Research Part B 46 (2012) 381–388
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Airport complementarity: Private vs. government ownership and welfare gravitation Benny Mantin ⇑ Dept. of Management Sciences, University of Waterloo, 200 University Avenue West, Waterloo, ON, Canada N2L 3G1
a r t i c l e
i n f o
Article history: Received 5 May 2011 Received in revised form 2 October 2011 Accepted 2 October 2011
Keywords: Airports Private ownership Public ownership Complementarity
a b s t r a c t We study the effects of airport ownership (private vs. government) on welfare in the presence of airport complementarity, where each airport is located in a different country. Considering Cournot competition in the airline market, the unique Nash equilibrium is such that the two countries privatize their airports, even though both countries are better off, from a welfare perspective, with public (government-owned) airports. Considering a differentiated Bertrand competition in the airline market, the same result prevails if the cross price elasticities are sufficiently high, otherwise the symmetric government-ownership of airports may also be a Nash equilibrium. Ó 2011 Elsevier Ltd. All rights reserved.
1. Introduction Until the mid 1980s, airports around the world were government owned and operated. The privatization of the British Airports Authority (BAA), in the UK, in 1986 was the initial move in the airport sector to change the governance structure.1 This move was part of a larger reform package that also saw telecommunications, rail and water infrastructure privatized in the UK. The broader geographic shift to airport privatization was set off by a variety of factors. These factors include the realization that airports are now a mature industry and can be economically self-sufficient, airports can generate large revenues from non-aeronautical and commercial activities, there is greater pressure from airport users for operational and economic efficiencies, and finally, the fact that governments have been unable to raise the funds required to finance airport infrastructure (Odoni, 2009). Airports operated as public utilities prior to the privatization shift and hence there was a perception that they were (local) monopolies. As a result, when privatization of airport ownership occurred, there was naturally some discussion on whether airport pricing, service provision, investment and management, would require some oversight. Privately held airports would seek to maximize profits – the return to shareholder equity, as they should, but this, some argued, could reduce overall social welfare. The question was should some form of price regulation be imposed.2 Different countries chose different paths regarding privatization, both in how, and whether, to regulate any such privatized infrastructure. These differences provided a fertile basis for researchers, both empirical and methodological, to investigate outcomes and to explain why some outcomes might or did arise; an extensive literature emerged.
⇑ Tel.: +1 519 888 4567x32235; fax: +1 519 746 7252. 1 2
E-mail address: [email protected] See de Neufville and Odoni (2003) and Gillen (2011), for reviews. There are four types of price regulation: single till, dual till, rate of return, and price monitoring (Gillen, 2011).
0191-2615/$ - see front matter Ó 2011 Elsevier Ltd. All rights reserved. doi:10.1016/j.trb.2011.10.001
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Basso and Zhang (2007) synthesize the literature on airport pricing into two broad modeling approaches,3 and they recognize that the mainstream literature has treated airports in isolation (Zhang and Zhang, 1997, 2001, 2003; Czerny, 2006; Brueckner, 2002). In this literature, an airport system generally consists of the regulator (or government) who seeks to maximize social welfare, the airport itself, which is either privately owned (and seeks to maximize profit) or government owned (and seeks to maximize social welfare), and the users of the airport (passengers and airlines). In this literature the network aspect of an airport has been ignored. However, airports are part of a larger system where each airport is a node being connected by airline(s) to another node. Airports provide complementary service to all of those airports to which they are connected: two airports are required to facilitate airborne trips – one at the origin and one at the destination. Basso and Zhang argue that, ‘‘failure to consider the complementarities when looking for optimal pricing policies will result in social welfare losses.’’ Yet, this observation has been largely overlooked and understudied. Specifically, the effects of the airport governance mode—public vs. private ownership—with airport complementarity is not yet understood with respect to the welfare outcome or even with regard to decisions regarding privatization or regulation. Simply put the network aspect of an airport has not been considered in evaluating changes in governance or regulation. Only a handful of papers have considered airports with complementary services (Basso, 2008; Pels and Verhoef, 2004; Czerny, 2007; Oum et al., 1996; Brueckner, 2005). However, these papers generally deal with congestion tolls that have been imposed on airport users, and they generally do not discuss the government decisions as to whether to keep the airport under government ownership or to privatize the airport.4 Kawasaki (2011) assumes two airports in the same country and studies a related question: whether an airport should be under national government ownership or under local government ownership. These two types of ownership are prevalent in Japan. In our study we consider airports in separate countries and allow for airport privatization. In this paper the emphasis is on examining the decision whether to keep an airport under government ownership or to privatize it, taking into account airport complementarity. Two related important issues emerge. First, with airport complementarity, welfare gravitation may occur. Welfare gravitation is an important concept introduced in the paper and can be explained in the following way. Consider a system of two airports where one is government owned and the other is private. The government owned airport sets low charges (prices at marginal cost) to stimulate demand and generate welfare for passengers and airlines from that location (i.e., country). The privately held airport may take advantage of the low charges set by the government owned airport. The private airport, in return, sets high charges that maximize its profit. These high charges extract some benefits available to passengers and airlines by the pricing behavior of the government owned airport. Since the airport extracts additional profit from the passengers and the airline of the other location, we observe ‘gravitation of welfare’ from one location (the country with the government owned airport) to the other (the country with the private airport). Secondly, the paper considers the issue that an airport under government ownership may not necessarily result in the socially optimal outcome. A government owned airport, though it seeks to maximize welfare, may experience a level of social welfare that is lower than if the airport was private. This outcome is a direct result of airport complementarity and the effect of welfare gravitation. For example, if two airports in the system are owned by their governments, each government may have the incentive to privatize its airport in order to take advantage of welfare gravitation and increase local welfare. If one airport is private, the government of the other country has the incentive to privatize its airport as well to offset the negative effect of welfare gravitation and recover some welfare. This paper considers a system with two complementary airports, each belonging to a different jurisdiction (for example, a country), and hence controlled or regulated by a different decision maker. The airports are served by two competing airlines who interact either in a Cournot or a differentiated Bertrand type of competition. Cournot competition reflects a situation where the two airlines are perceived as perfect substitutes. That is, the two airlines provide an identical service. By contrast, differentiated Bertrand competition may indicate a scenario where the two airlines offer different services or, more importantly, a situation where passengers have some preference for one airline (the home airline) over the other (the airline from the other country).5 The governments of the two countries seek to maximize, separately, the welfare of their countries. The choice the government is faced with is to either keep the ownership of the airport public, or to privatize. A public airport seeks to maximize welfare, which is the sum of the airport profit, the profit of the airport from that country and the surplus of the passengers from that country. A private airport sets the airport charges to maximize own profit only. Once the airport charges are set, the two airlines set their quantities (if they are engaged in Cournot competition) or their airfares (if they are engaged in a differentiated Bertrand competition) and demand is realized. In the presence of airport complementarity, when airlines compete in a Cournot type of competition, we find that both countries are best off, in terms of welfare, if airports are kept under government ownership (i.e., manage their airports as welfare maximizers).6 However, each country has an incentive to deviate from this state where both airports are public, and to privatize its own airport, as such a move is welfare improving. This improvement is achieved due to welfare gravitation from
3 In their survey paper, Basso and Zhang divided the contributions into two broad categories. In the first category—the traditional approach—which yields partial equilibrium, the demand for airport services is not formally modeled and airlines’ decisions are not directly modeled (Morrison and Winston, 1989; Oum and Zhang, 1990). In the second category the airline market is formally modeled—the vertical structure approach (Brueckner, 2002; Zhang and Zhang, 2006). 4 In one of the extensions in his work, Basso (2008) considers two independent profit maximizing airports to highlight the effect of double marginalization and capacity over investment. 5 Brueckner and Proost (2010). 6 We shall note that further improvement in welfare can be achieved when the system is centralized. This is consistent with Pels and Verhoef (2004).
B. Mantin / Transportation Research Part B 46 (2012) 381–388
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Fig. 1. Market structure and decisions: Cournot competition
the country with the government owned airport to the country with the private airport. When one airport is privately owned, the other country follows suit and privatizes its airport as well to avoid the perils of welfare gravitation. Thus, the unique Nash equilibrium is the state where both countries privatize their airports, even though both are better off when the two airports are public. In other words, they are trapped in a situation similar to the Prisoners’ Dilemma. When airlines are engaged in a differentiated Bertrand competition, we find that if the cross price elasticity is sufficiently high, the same result prevails. Namely, the unique Nash equilibrium is the state where both countries privatize their airports. However, when the cross price elasticity is low, there exist two symmetric Nash equilibria: one in which both airports are public and one where both are private. These results suggest that regulations of airport charges need to carefully account for airport complementarity. Specifically, limiting the toll a private airport is allowed to charge could be detrimental to the welfare of this country, as this may allow the other airport to raise its own charges and gravitate welfare. Possibly, some contingent tolls could be proposed but are harder to implement. Governments, then, may wish to reconsider their airport privatization efforts, and engage in better coordination of the regulation of the charges set by the airports. In Section 2 we introduce the model and we analyze the scenario where the airlines are engaged in a Cournot type of competition. In Section 3 we consider the case where the two airlines compete in a differentiated Bertrand competition. Section 4 concludes. 2. Cournot competition 2.1. The model Consider a market consisting of two nodes and a single link connecting these two nodes as illustrated in Fig. 1. Each node represents an airport (equally likely, it could be any other transportation node such as a seaport and train hub) in a separate country. The link is served by two competing airlines, each based in a different country. Demand exists equally in each country to travel (or to ship goods) to the other country. The governments of each of these two countries seek to maximize the welfare of their own country. The welfare of each country is the sum of the consumer surplus, the airline profit, and the airport profit of that country. In the first stage, each government decides which ownership type to adopt for its airport, which could be either government ownership (GO) or private ownership (PO). Under government ownership, the airport remains as a public utility and is managed by the government. Under the private ownership, the government privatizes the airport, and the resulting entity aims to maximize its own profit only. Once the airport ownership types have been selected, the two airports simultaneously set their airport charges. Consistent with the literature, we assume these charges, which are charged to the airlines, are passed onto the passengers and levied onto the airfare.7 Thus, we consider airport passenger fees, by letting Fi, i 2 {1, 2}, denote the passenger fee charged by airport i to all passengers using this airport.8 Note that each passenger needs to pay fees to both airport, F1 and F2, as the airports provide a complementary service and both need to be consumed in order to complete the trip. Given the passenger fees, in the last stage, the two airlines set their quantities, q1 and q2, as they engage in a Cournot type of competition, and demand is realized. Let pCi denote the fare paid by passengers from country i (the superscript C is for carrier). The demand for travel in country i follows a down-sloping curve with Qi = 1 Pi where Qi is the total quantity released to this market by both airlines and Pi is the full price paid by passengers for travel.9 Specifically, the full price paid by passengers of country i is the sum of the fare, pCi , and the two airport fees, F1 and F2, i.e., Pi ¼ pCi þ F 1 þ F 2 . We assume that the demand stemming from each country is for a round trip (such as is the case with passenger airlines). When demand is for round trips, demand from the two countries can be perceived as substitutable (from the airlines’ per7
Assuming exogenous load factors (see, e.g., Brueckner, 2002) airport landing fees are equivalent to airport passenger fees. In what follows,we can further study the case where a welfare-maximizing airport may employ a discriminatory pricing policy in the sense that passengers from the two different countries could be charged different fees (à la Pels and Verhoef, 2004). See also Footnote 11. 9 This simple linear demand function is adopted to avoid unnecessary complications in the analysis. The model can be generalized to a broader class of demand functions. 8
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B. Mantin / Transportation Research Part B 46 (2012) 381–388
Fig. 2. The demand in the two countries
spective), as the two demands compete for the same supply of products. Consequently, the total quantity supplied by the two airlines is shared by the demands from both countries.10 More precisely, quantity is shared by passengers from both countries to the point where prices in both markets are equal. Since the products are shared by both markets, in equilibrium, passengers from both countries pay the same fare exactly, pC1 ¼ pC2 pC . Note also, that passengers from both countries pay the same total fare Pi = P2 = pC + F1 + F2, where pC is the base airfare and F1 and F2 are the fees paid to the two airports. Thus, the demand in country i, i 2 {1, 2}, is Qi = 1 Pi = 1 Fi Fj pC. The demand from both countries is added up to yield the total demand function
Q ¼ Q i þ Q j ¼ 2ð1 ðF i þ F j Þ pC Þ;
ð1Þ
where Q = q1 + q2 is the sum of quantities set by the two airlines. We assume zero costs for the airline, so Airline i’s profit is given by PCi ¼ qi pC . Similarly, we assume zero cost for the airports, hence Airport i’s profit is given by PAi ¼ F i ðQ i þ Q j Þ. The surplus of consumers from country i is given by R Pmax i CSi ¼ P Q i ðPi ÞdPi ¼ 12 ð1 pC F i F j Þ2 ; j – i. A private airport maximizes only its own profit PAi ; i 2 f1; 2g, when setting i the passengers’ fees, while a public (government owned) airport maximizes the total welfare of the country associated with travel: W i ¼ PAi þ PCi þ CSi ; i 2 f1; 2g. The demand curves are illustrated in Fig. 2, wherein we denote by PAij the profit of airport i from passengers of country j, where i, j 2 {1, 2}. Consider, for example, the demand in Country 1. The total supply in this country is Q1 and the area under the demand curve up to this point is segmented into four components: the consumers’ surplus, the profit of Airport 1 from the passengers stemming from Country 1 PA11 , the profit of Airport 2 from the passengers stemming from Country 1 PA21 , and the airlines’ combined profit from these passengers. In the latter case one can further break down the profit between the two airlines. Note that this figure depicts a symmetric scenario. However, apart from the airfare, pC, and the total full fare paid by passengers, P1 = P2, the realizations in the two countries can differ. Specifically, the two airports may charge the passengers quite differently. 2.2. Model analysis We solve the model backward to yield the subgame perfect Nash equilibrium. We first derive the airlines’ optimal quantity decisions, then we obtain the airports’ fees to passengers for the different airport management regimes. We conclude with governments’ choice of the optimal regimes for their airports. We consider each of the airport ownership cases separately (both are government owned, both are privately owned, one is government owned and the other is privately owned). 2.2.1. Both airports are privately owned (PO–PO) Consider the case where both airports are privately owned, i.e., they set fees to maximize their respective profits. From (1) we have that pC ¼ 1 F i F j 12 ðqi þ qj Þ. Solving backward, in the final stage, the two airlines simultaneously set their quantities to maximize their profits, PCi ¼ qi pC ; i 2 f1; 2g, yielding qi ¼ 23 ð1 F i F j Þ; i – j 2 f1; 2g. Proceeding with the second stage, the two airports simultaneously maximize their profits, PAi ¼ ðq1 þ q2 ÞF i , resulting in F 1 ¼ F 2 ¼ 13. Hence, when both 2 4 2 airports are profit maximizers, we have pC ¼ 19 ; qi ¼ 29 ; PCi ¼ 81 ; PAi ¼ 27 ; CSi ¼ 81 , and W i ¼ 16 . These results are reported 81 in Table 1.
10 One can also consider the case of one way trip demand where the demand originating from each country is directional (such as cargo)—ending at the destination country. Since the airlines’ fleets operate in both directions, the total quantity supplied by both airlines is the same in each market. The insights from such a model are generally in line with the round trip assumption developed here.
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B. Mantin / Transportation Research Part B 46 (2012) 381–388 Table 1 Results for the return trip model. Cases
F1
F2
pC
qi
PCi
PA1
PA2
CSi
W1
W2
1:PO, 2:PO
1 3 1 7 1 5
1 3 3 7 1 5
1 9 1 7 1 5
2 9 2 7 2 5
2 81 2 49 2 25
4 27 4 49 4 25
4 27 12 49 4 25
2 81 2 49 2 25
16 81 8 49 8 25
16 81 16 49 8 25
1:GO, 2:PO 1:GO, 2:GO
¼ 0:197 ¼ 0:163 ¼ 0:32
¼ 0:197 ¼ 0:326 ¼ 0:32
Where PO stands for private ownership and GO for government ownership; i 2 {1, 2}.
Table 2 Welfare analysis with Cournot competition.
1:PO 1:GO
2:PO
2:GO
0.197, 0.197 0.163, 0.326
0.326, 0.163 0.32, 0.32
Where PO stands for private ownership and GO for government ownership.
2.2.2. One airport is government owned and the other is privately owned (GO–PO) Now, assume that, without loss of generality, Country 1 decides to adopt government ownership for its airport (while Country 2’s airport is privately owned). The analysis of the third stage for the GO–PO case coincides with the corresponding analysis in the case where both airports are privately owned (PO–PO). In the second stage, the airport in Country 1 seeks to maximize the welfare of the country, W1, rather than the airport profit only. Solving simultaneously, we obtain F 1 ¼ 17 and F 2 ¼ 37. Intuitively, to increase welfare, the public airport will reduce the fees charged to the passengers; however, the private airport will take advantage of this and increase its fee to passengers. Since quantity is shared to the level where total price in both countries is identical, due to demand symmetry, the only difference between the two countries stems from the airports’ 2 4 profits (i.e., consumer surplus and airline profit are the same in both countries). We have pC ¼ 17 ; qi ¼ 27 ; PCi ¼ 49 ; PA1 ¼ 49 ; 2 8 16 PA2 ¼ 12 ; CS ¼ ; W ¼ and W ¼ . The public airport (Airport 1) sets the passenger fee such that it transfers surplus 1 2 i 49 49 49 49 from the airport to the passengers. However, by doing so, it transfers surplus not only to its own local passengers, but also to the foreign passengers from the other country (Country 2).11 The other airport (Airport 2) takes advantage of this pricing by raising its own fees (and note, in Table 1, that the fees that this airport charges are higher than when both airports are privately owned). From consumers’ perspective, the former effect—the transfer of surplus from airport to passengers—dominates, as the total price decreases and their surplus improves. Yet, Country 1 suffers from a significant decrease in welfare due to the corresponding pricing by the other airport, Airport 2. The above analysis yields the following lemma. Lemma 1. Consider Cournot competition in the airline market. Assume that both airports are privately owned. A unilateral deviation from private ownership airport to government ownership by one of the countries has a detrimental effect on the welfare of the deviating country and a positive effect on the welfare of the other country. Proof. When both airports are private, the welfare of each country is 16 ¼ 0:197. If one airport is welfare maximizing and the 81 8 other is profit maximizing, their profits are 49 ¼ 0:163 and 16 ¼ 0:326, respectively. Since 0.163 < 0.197 and 0.326 > 0.197, the 49 country deviating from symmetric private airport ownership to government ownership is worse off, while the other country, which stays with a privately owned airport, is better off. h This is an important result. It reveals that if all airports were to be privatized, countries would face serious difficulties in returning to government ownership. A unilateral move from private to public ownership is not a move that improves welfare for the country that is initiating the move, hence it is not an acceptable move from a welfare perspective. Not only would it worsen the welfare of the country that changes its airport ownership type to public, it also improves the welfare of the country that stays with private ownership. Essentially, when such a move is adopted, we witness mobilization of welfare from one country (with the government owned airport) to the other (with the privately owned airport)—a concept to which we refer as welfare gravitation. 2.2.3. Both airports are privately owned (GO–GO) Lastly, if Country 2 follows suit and adopts government ownership for its airport as well, solving the model back2 4 2 8 wards,using the same stages shown above, we have F 1 ¼ F 2 ¼ 15 ; pC ¼ 15 ; qi ¼ 25 ; PCi ¼ 25 ; PAi ¼ 25 ; CSi ¼ 25 , and W i ¼ 25 . The different outcomes of the different cases are summarized in Table 1. 11 One way to mitigate this effect is to price discriminate between the passengers based on their point of origin (similar to Pels and Verhoef, 2004 who discriminate the airlines based on their origin). Surprisingly, however, such price discrimination is not welfare improving.
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B. Mantin / Transportation Research Part B 46 (2012) 381–388 Table 3 Welfare analysis in the differentiated Bertrand competition.
1:PO 1:GO
2:PO
2:GO
ð117bÞ ; ð117bÞ 9ð2bÞ2 ð1bÞ 9ð2bÞ2 ð1bÞ 4ð5bÞ ; 4ð117bÞ 9ð3bÞ2 ð1bÞ 9ð3bÞ2 ð1bÞ
4ð117bÞ ; 4ð5bÞ 9ð3bÞ2 ð1bÞ 9ð3bÞ2 ð1bÞ 5b 5b 9ð1bÞ ; 9ð1bÞ
Where PO stands for private ownership and GO for government ownership.
Even though both countries are better off in terms of welfare if they were both to adopt government ownership for their airports, they do not reach such an equilibrium, as they always have the incentive to deviate and privatize their airports. Specifically, if one country adopts government ownership for its airport, then the other country always chooses to privatize its airport. This ownership structure gravitates welfare from one country to the other and improve welfare, even if only marginally. This is summarized in the following theorem. Theorem 1. Consider Cournot competition in the airline market. The two countries find themselves in a Prisoner’s Dilemma type of inferior equilibrium with regard to the airport ownership types; even though both are better off with public (welfare maximizing) airports, they end up in the Pareto inferior Nash equilibrium where both airports are private (profit maximizers). Proof. Lemma 1 already established the fact that a deviation from the symmetric PO is not welfare improving, hence, it is a Nash equilibrium. We make use of Table 2 which summarizes the welfare outcomes in the different states. In Table 2, one can observe that from the symmetric GO a unilateral deviation by either country to PO is welfare improving. That is, the best reaction of each country is always to adopt PO. Hence, the Nash equilibrium is the symmetric PO regime. It is evident from Table 2 that symmetric PO is the Pareto inferior equilibrium and that both countries would be better off under the symmetric GO. h The focal point then is to privatize the airports even though the symmetric state where both airports are privately owned results in an inferior welfare outcome for both countries. This result suggests a ripple effect. Though we have not studied more elaborate networks of multiple countries and several airports, it appears that once a country privatizes its airport(s), others will follow along and adopt private ownership for their airports. If both airports are privately owned, welfare improvement for both countries is attained only when both adopt government ownership for their airports. Far sighted governments may realize that unilaterally deviating from the symmetric government ownership state and adopting a private ownership could ultimately be detrimental as the other country may follow suit and will adopt the same ownership type, leading both countries to experience a decrease in their welfare. Hence, such governments might consider agreements that ensure that both countries will manage their airports as public entities. However, such agreements may be interpreted as interfering with each other’s governance, and therefore are less likely to be adopted. 3. Differentiated Bertrand competition In the previous section we assumed that the airlines were engaged in a Cournot competition. Such a competition implies that the airlines are perceived by passengers as perfect substitutes, in which case airlines compete over quantities. In this section we relax this assumption and instead we assume that the two airlines are engaged in a differentiated Bertrand competition. This implies that the substitution between the two airlines is imperfect and the products are differentiated. We abstract away from airlines’ differentiation decisions as such a differentiation in our setting could stem from passengers’ preference for flying with the airline from the same country (i.e., patriotic preference as is, e.g., in Brueckner and Proost, 2010). In a differentiated Bertrand competition, airlines choose their fares and can further price fares differently for passengers based on their origin country. Let Qik and denote the round trip demand originating in Country i (to Country j) for flying with Airline k and let Pik denote the full fare paid by passengers for this trip. This full fare is composed of the airfare, pik, and the passenger fees from both airports, F1 and F2, i.e., Pik = pik + F1 + F2. The demand stemming from Country i for flying with Airline k is given by Qik = 1 Pik + bPil, b < 1, i 2 {1, 2}, k – l 2 {1, 2}.12 The first two stages are as before: in the first stage, the two countries independently choose the ownership type for their airports, and, in the second stage, each airport sets the passenger fees. In the third stage, the two airlines set their airfares and demand is realized. The analysis of the differentiated Bertrand competition is very similar to the Cournot competition model. For brevity, we do not repeat the entire analysis and we merely review the primary steps and highlight the main insights. Solving backward, in the third stage the two airlines simultaneously set their prices to maximize their respective profits, PCk ¼ p1k Q 1k þ 2 ÞþbðF 1 þF 2 Þ p2k Q 2k ; k 2 f1; 2g, yielding pik ¼ 1ðF 1 þF2b ; i; k 2 f1; 2g. 12 Note that this formulation can be easily generalized to account for possible price discrimination between the passengers based on their point of origin (by assuming different demand intercepts, own and cross price elasticities). However, here we impose symmetry to simplify the presentation and insights.
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B. Mantin / Transportation Research Part B 46 (2012) 381–388
Next, we solve the airports’ optimal passenger fees. If both airports are privately owned, then both airports simultaneously ð117bÞ 1 maximize their profits, PAi ¼ ðQ 11 þ Q 12 þ Q 21 þ Q 22 ÞF i , resulting in F 1 ¼ F 2 ¼ 3ð1bÞ , in which case W 1 ¼ W 2 ¼ 9ð2bÞ . If 2 ð1bÞ
both airports are government owned, they simultaneously seek to maximize their welfare, W i ¼ PAi þ PCi þ CSi ,13 in which 1þb 5b with W 1 ¼ W 2 ¼ 9ð1bÞ . If one airport is government owned and the other is privately owned, then the govcase F 1 ¼ F 2 ¼ 6ð1bÞ 2ð2bÞ 1þb , while the privately owned airport sets 3ð3þb , where the former country gets a ernment owned airport sets a fee of 3ð1bÞð3bÞ 2 4bÞ
welfare of
4ð5bÞ 9ð3bÞ2 ð1bÞ
and the latter obtains a welfare of
4ð117bÞ . 9ð3bÞ2 ð1bÞ
These results are summarized in Table 3.
With p symmetric government ownership, a country has an incentive to deviate and privatize its airport if ffiffiffi b > 5 2 6 0:101. From this state, the other country, whose airport is still owned by the government, always has an incentive to defect as well and privatize its airport as well. This gives rise to the following statement. pffiffiffi Theorem 2. Consider differentiated Bertrand competition in the airline market. If b > 5 2 6 0:101, then the two countries find themselves in a Prisoner’s Dilemma type of inferior equilibrium with regard to the airport ownership type; though both are better off with public (welfare maximizing) airports, they both employ the pffiffiffi unique Pareto inferior Nash equilibrium where both airports are privately owned (profit maximizers); otherwise, if b < 5 2 6 0:101, then there exist two subgame perfect Nash equilibria: either both privatize their airports or both keep them as public utilities.
Proof. It follows from Table 3: a unilateral deviation by, say Country 1, from {PO, PO} to {GO, PO} is never beneficial, since 4ð5bÞ > 9ð3bÞ , so {PO, PO} is a candidate for NE. Since a unilateral deviation by, say Country 1, from {GO, GO} to {PO, 2 ð1bÞ pffiffiffi pffiffiffi 4ð117bÞ 5b > 9ð1bÞ ) b > ð5 2 6Þ, {PO, PO} is the unique Nash equilibrium if b > 5 2 6, otherGO} is beneficial only if 9ð3bÞ 2 ð1bÞ
ð117bÞ 9ð2bÞ2 ð1bÞ
wise, both {PO, PO} and {GO, PO} are Nash equilibria. It is evident that {GO, GO} is preferred by both over {PO, PO} since 5b 9ð1bÞ
ð117bÞ > 9ð2bÞ always holds true, establishing that {PO, PO} is the inferior Pareto equilibrium in this scenario. 2 ð1bÞ
h
To gain insight into this result, first consider the equilibrium state, which is symmetric private ownership. If one of the countries unilaterally deviates to government ownership for its airport, it reduces the passenger fees while the other airport, which is privately owned, takes advantage of this pricing decision and increases its own fees (yet, the sum of the fees drops). The difference in passenger fees results from welfare gravitation from one country to the other. With this deviation (of one airport from PO to GO), the base airfare increases, yet the full airfare decreases (as the decrease in passenger fees dominates the increase in airfare), so consumers are better off. As the airfare increases, despite the decrease in full airfare, the airlines’ profits increase. Lastly, due to the decrease in fees, the profit of the GO airport is lower than under the symmetric PO state. This decrease is so substantial that it dominates the combined increase in consumer surplus and the airline’s profit, implying that a deviation from symmetric PO state is not beneficial to either country. Now, consider the symmetric government ownership. If one country unilaterally deviates to PO, it raises the passenger fees, taking advantage of the decrease in fees at the GO airport (yet, the sum of passenger fees decreases). The base fare decreases, yet the total fare increases, resulting in a decrease in airlines’ profits. The deviating country (now with PO airport) experiences an increase in airport profit. When b is sufficiently high (i.e., substitution is high) the increase in airport profit dominates the decrease in consumer surplus and the airline’s profit. Hence, a defection from the symmetric GO occurs, facilitating a corresponding move by the other country, ultimately resulting with the symmetric PO equilibrium. 4. Concluding remarks This work contributes to the limited literature that considers airport complementarity, contrasted with the widespread modeling approach where airports are studied independently. Particularly, we are interested in the decision process—modeled as a game theoretic process—of privatizing airports vs. keeping them as public entities under government ownership. In the absence of airport complementarity, a publicly owned airport naturally yields welfare maximization. Here, we showed that when two airports provide a complementary service, each in a different country, publicly owned airports do not necessarily result in welfare maximization. Specifically, the best option for each country to take is to privatize its airport (except when cross price elasticities are low, when the airlines are engaged in a differentiated Bertrand competition). Indeed, if both airports are publicly owned, both countries could be better off in terms of welfare. Yet, the unique subgame perfect Nash equilibrium is the state where both countries privatize their airports, which is a Pareto inferior equilibrium. This result has been shown to be robust as it holds both for Cournot competition and differentiated Bertrand competition (except when cross price elasticities are low, in which case there exists two symmetric Nash equilibria). This work has explored the importance of the inclusion of complementarity effects on airport ownership modes. This aspect shall play a major role in considering and evaluating bilateral and multilateral agreements. For example, the results of 13
In this differentiated Bertrand competition model, consumer surplus in Country i is is the vector of prices.
P R max pik k
pik
Q ik ðpÞdp ¼
P
1 k 2 ð1
þ bpil pik Þð1 pik þ bpil Þ; l – k, where p
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this paper are very important for the issue of open skies, as most European airports are, or are being, privatized, while in the US they are publicly owned. This work can be extended in many important ways. For example, larger networks can be considered where additional airports exist. Such airports could be hubs (or gateways) or end nodes connecting to the hubs. In such a scenario, the decision space expands dramatically as a country may choose to privatize some of its airports while keeping the remaining airports as public entities. When accounting for larger networks, one can also consider more than two countries. However, such a generalization is expected to amplify the results of this work, as the adoption of government ownership for an airport, while all others are under private ownership, may result in welfare gravitation to more than one country. Importantly, one can also consider another regulatory decision: whether to let the two competing airlines merge (or collaborate) and act as a monopoly in this market. Lastly, we have abstracted away from airport concession income.14 Modeling such non-aeronautical income is challenging in the presence of multiple airports: can it be consumed at any of the airports (in which case the airports compete over this service) or can it be consumed only at one end of the trip (such as car rental, and in this case the service is complementary). Acknowledgments The author thanks David Gillen for his valuable feedback and Lorra Ward. This research was supported by a Natural Sciences and Engineering Research Council of Canada (NSERC) grant and by the Transport Canada support for research under the Asia–Pacific Gateway and Corridor Initiative provided by the Center for Transportation Studies at the University of British Columbia. The author is also grateful for the constructive feedback provided by the two referees, which has significantly improved the paper. References Basso, Leonardo, 2008. Airport deregulation: effects on pricing and capacity. International Journal of Industrial Organization 26 (4), 1015–1031. Basso, Leonardo, Zhang, Anming, 2007. An interpretative survey of analytical models of airport pricing. In: Lee, Daren (Ed.), Advances in Airline Economics, vol. 2. Elsevier Publishers, Netherland. Brueckner, Jan K., 2002. Airport congestion when carriers have market power. American Economic Review 92 (5), 1357–1375. Brueckner, Jan K., 2005. Internalization of airport congestion: a network analysis. International Journal of Industrial Organization 23 (7–8), 599–614. Brueckner, Jan K., Proost, Stef, 2010. Carve-outs under airline antitrust immunity. International Journal of Industrial Organization 28 (6), 657–668. Czerny, Achim I., 2006. Price-cap regulation of airports: single-till versus dual-till. Journal of Regulatory Economics 30 (1), 85–97. Czerny, Achim I., 2007. Congestion Management Under Uncertainty in a Two-airport System. Working paper, Berlin University of Technology. de Neufville, Richard, Odoni, Amedeo, 2003. Airport Systems: Planning, Design and Management. McGraw-Hill, New York. Gillen, David, 2011. The evolution of airport ownership and governance. Journal of Air Transport Management 17 (1), 3–13. Kawasaki, Akio, 2011. Comparison of National-Ownership and Local-Ownership Airports. Working Paper, Kagoshima University. Morrison, Steven, Winston, Clifford, 1989. Enhancing the Performance of the Deregulated Air Transportation System. Brookings Papers on Economic Activity, Microeconomics, 61–123. Morrison, William G., 2009. Real estate, factory outlets and bricks: a note on non-aeronautical activities at commercial airports. Journal of Air Transport Management 15 (3), 112–115. Odoni, Amedeo, 2009. The international institutional and regulatory environment. In: Belobaba, Peter, Odoni, Amedeo, Barnhart, Cynthia (Eds.), The Global Airline Industry. Wiley. Oum, Tae H., Zhang, Yimin M., 1990. Airport pricing – congestion tolls, lumpy investment, and cost recovery. Journal of Public Economics 43 (3), 353–374. Oum, Tae H., Zhang, Anming., Zhang, Yimin M., 1996. A note on optimal airport pricing in a Hub-and-spoke system. Transportation Research Part B 30 (1), 11–18. Pels, Eric, Verhoef, Erik, 2004. The economics of airport congestion pricing. Journal of Urban Economics 55 (2), 257–277. Starkie, David, 2001. Reforming UK airport regulation. Journal of Transport Economics and Policy 35 (1), 119–135. Zhang, Anming, Zhang, Yimin, 1997. Concession revenue and optimal airport pricing. Transportation Research Part E 33 (4), 287–296. Zhang, Anming, Zhang, Yimin, 2001. Airport charges, economic growth and cost recovery. Transportation Research Part E 37 (1), 25–33. Zhang, Anming, Zhang, Yimin, 2003. Airport charges and capacity expansion: effects of concessions and privatization. Journal of Urban Economics 53 (1), 54–75. Zhang, Anming, Zhang, Yimin, 2006. Airport capacity and congestion when carriers have market power. Journal of Urban Economics 60 (2), 229–247. Zhang, Anming, Zhang, Yimin, 2010. Airport capacity and congestion pricing with both aeronautical and commercial operations. Transportation Research Part B 44 (3), 404–413.
14 Studying airports’ concession income is gaining increasing attention. Due to the complementarity between airside and commercial revenues airports may have less incentive to abuse their power. See, e.g., the works by Starkie (2001), Morrison (2009), and Zhang and Zhang (2010).
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Airport complementarity: Private vs. government ownership and welfare gravitation Benny Mantin ⇑ Dept. of Management Sciences, University of Waterloo, 200 University Avenue West, Waterloo, ON, Canada N2L 3G1
a r t i c l e
i n f o
Article history: Received 5 May 2011 Received in revised form 2 October 2011 Accepted 2 October 2011
Keywords: Airports Private ownership Public ownership Complementarity
a b s t r a c t We study the effects of airport ownership (private vs. government) on welfare in the presence of airport complementarity, where each airport is located in a different country. Considering Cournot competition in the airline market, the unique Nash equilibrium is such that the two countries privatize their airports, even though both countries are better off, from a welfare perspective, with public (government-owned) airports. Considering a differentiated Bertrand competition in the airline market, the same result prevails if the cross price elasticities are sufficiently high, otherwise the symmetric government-ownership of airports may also be a Nash equilibrium. Ó 2011 Elsevier Ltd. All rights reserved.
1. Introduction Until the mid 1980s, airports around the world were government owned and operated. The privatization of the British Airports Authority (BAA), in the UK, in 1986 was the initial move in the airport sector to change the governance structure.1 This move was part of a larger reform package that also saw telecommunications, rail and water infrastructure privatized in the UK. The broader geographic shift to airport privatization was set off by a variety of factors. These factors include the realization that airports are now a mature industry and can be economically self-sufficient, airports can generate large revenues from non-aeronautical and commercial activities, there is greater pressure from airport users for operational and economic efficiencies, and finally, the fact that governments have been unable to raise the funds required to finance airport infrastructure (Odoni, 2009). Airports operated as public utilities prior to the privatization shift and hence there was a perception that they were (local) monopolies. As a result, when privatization of airport ownership occurred, there was naturally some discussion on whether airport pricing, service provision, investment and management, would require some oversight. Privately held airports would seek to maximize profits – the return to shareholder equity, as they should, but this, some argued, could reduce overall social welfare. The question was should some form of price regulation be imposed.2 Different countries chose different paths regarding privatization, both in how, and whether, to regulate any such privatized infrastructure. These differences provided a fertile basis for researchers, both empirical and methodological, to investigate outcomes and to explain why some outcomes might or did arise; an extensive literature emerged.
⇑ Tel.: +1 519 888 4567x32235; fax: +1 519 746 7252. 1 2
E-mail address: [email protected] See de Neufville and Odoni (2003) and Gillen (2011), for reviews. There are four types of price regulation: single till, dual till, rate of return, and price monitoring (Gillen, 2011).
0191-2615/$ - see front matter Ó 2011 Elsevier Ltd. All rights reserved. doi:10.1016/j.trb.2011.10.001
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Basso and Zhang (2007) synthesize the literature on airport pricing into two broad modeling approaches,3 and they recognize that the mainstream literature has treated airports in isolation (Zhang and Zhang, 1997, 2001, 2003; Czerny, 2006; Brueckner, 2002). In this literature, an airport system generally consists of the regulator (or government) who seeks to maximize social welfare, the airport itself, which is either privately owned (and seeks to maximize profit) or government owned (and seeks to maximize social welfare), and the users of the airport (passengers and airlines). In this literature the network aspect of an airport has been ignored. However, airports are part of a larger system where each airport is a node being connected by airline(s) to another node. Airports provide complementary service to all of those airports to which they are connected: two airports are required to facilitate airborne trips – one at the origin and one at the destination. Basso and Zhang argue that, ‘‘failure to consider the complementarities when looking for optimal pricing policies will result in social welfare losses.’’ Yet, this observation has been largely overlooked and understudied. Specifically, the effects of the airport governance mode—public vs. private ownership—with airport complementarity is not yet understood with respect to the welfare outcome or even with regard to decisions regarding privatization or regulation. Simply put the network aspect of an airport has not been considered in evaluating changes in governance or regulation. Only a handful of papers have considered airports with complementary services (Basso, 2008; Pels and Verhoef, 2004; Czerny, 2007; Oum et al., 1996; Brueckner, 2005). However, these papers generally deal with congestion tolls that have been imposed on airport users, and they generally do not discuss the government decisions as to whether to keep the airport under government ownership or to privatize the airport.4 Kawasaki (2011) assumes two airports in the same country and studies a related question: whether an airport should be under national government ownership or under local government ownership. These two types of ownership are prevalent in Japan. In our study we consider airports in separate countries and allow for airport privatization. In this paper the emphasis is on examining the decision whether to keep an airport under government ownership or to privatize it, taking into account airport complementarity. Two related important issues emerge. First, with airport complementarity, welfare gravitation may occur. Welfare gravitation is an important concept introduced in the paper and can be explained in the following way. Consider a system of two airports where one is government owned and the other is private. The government owned airport sets low charges (prices at marginal cost) to stimulate demand and generate welfare for passengers and airlines from that location (i.e., country). The privately held airport may take advantage of the low charges set by the government owned airport. The private airport, in return, sets high charges that maximize its profit. These high charges extract some benefits available to passengers and airlines by the pricing behavior of the government owned airport. Since the airport extracts additional profit from the passengers and the airline of the other location, we observe ‘gravitation of welfare’ from one location (the country with the government owned airport) to the other (the country with the private airport). Secondly, the paper considers the issue that an airport under government ownership may not necessarily result in the socially optimal outcome. A government owned airport, though it seeks to maximize welfare, may experience a level of social welfare that is lower than if the airport was private. This outcome is a direct result of airport complementarity and the effect of welfare gravitation. For example, if two airports in the system are owned by their governments, each government may have the incentive to privatize its airport in order to take advantage of welfare gravitation and increase local welfare. If one airport is private, the government of the other country has the incentive to privatize its airport as well to offset the negative effect of welfare gravitation and recover some welfare. This paper considers a system with two complementary airports, each belonging to a different jurisdiction (for example, a country), and hence controlled or regulated by a different decision maker. The airports are served by two competing airlines who interact either in a Cournot or a differentiated Bertrand type of competition. Cournot competition reflects a situation where the two airlines are perceived as perfect substitutes. That is, the two airlines provide an identical service. By contrast, differentiated Bertrand competition may indicate a scenario where the two airlines offer different services or, more importantly, a situation where passengers have some preference for one airline (the home airline) over the other (the airline from the other country).5 The governments of the two countries seek to maximize, separately, the welfare of their countries. The choice the government is faced with is to either keep the ownership of the airport public, or to privatize. A public airport seeks to maximize welfare, which is the sum of the airport profit, the profit of the airport from that country and the surplus of the passengers from that country. A private airport sets the airport charges to maximize own profit only. Once the airport charges are set, the two airlines set their quantities (if they are engaged in Cournot competition) or their airfares (if they are engaged in a differentiated Bertrand competition) and demand is realized. In the presence of airport complementarity, when airlines compete in a Cournot type of competition, we find that both countries are best off, in terms of welfare, if airports are kept under government ownership (i.e., manage their airports as welfare maximizers).6 However, each country has an incentive to deviate from this state where both airports are public, and to privatize its own airport, as such a move is welfare improving. This improvement is achieved due to welfare gravitation from
3 In their survey paper, Basso and Zhang divided the contributions into two broad categories. In the first category—the traditional approach—which yields partial equilibrium, the demand for airport services is not formally modeled and airlines’ decisions are not directly modeled (Morrison and Winston, 1989; Oum and Zhang, 1990). In the second category the airline market is formally modeled—the vertical structure approach (Brueckner, 2002; Zhang and Zhang, 2006). 4 In one of the extensions in his work, Basso (2008) considers two independent profit maximizing airports to highlight the effect of double marginalization and capacity over investment. 5 Brueckner and Proost (2010). 6 We shall note that further improvement in welfare can be achieved when the system is centralized. This is consistent with Pels and Verhoef (2004).
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383
Fig. 1. Market structure and decisions: Cournot competition
the country with the government owned airport to the country with the private airport. When one airport is privately owned, the other country follows suit and privatizes its airport as well to avoid the perils of welfare gravitation. Thus, the unique Nash equilibrium is the state where both countries privatize their airports, even though both are better off when the two airports are public. In other words, they are trapped in a situation similar to the Prisoners’ Dilemma. When airlines are engaged in a differentiated Bertrand competition, we find that if the cross price elasticity is sufficiently high, the same result prevails. Namely, the unique Nash equilibrium is the state where both countries privatize their airports. However, when the cross price elasticity is low, there exist two symmetric Nash equilibria: one in which both airports are public and one where both are private. These results suggest that regulations of airport charges need to carefully account for airport complementarity. Specifically, limiting the toll a private airport is allowed to charge could be detrimental to the welfare of this country, as this may allow the other airport to raise its own charges and gravitate welfare. Possibly, some contingent tolls could be proposed but are harder to implement. Governments, then, may wish to reconsider their airport privatization efforts, and engage in better coordination of the regulation of the charges set by the airports. In Section 2 we introduce the model and we analyze the scenario where the airlines are engaged in a Cournot type of competition. In Section 3 we consider the case where the two airlines compete in a differentiated Bertrand competition. Section 4 concludes. 2. Cournot competition 2.1. The model Consider a market consisting of two nodes and a single link connecting these two nodes as illustrated in Fig. 1. Each node represents an airport (equally likely, it could be any other transportation node such as a seaport and train hub) in a separate country. The link is served by two competing airlines, each based in a different country. Demand exists equally in each country to travel (or to ship goods) to the other country. The governments of each of these two countries seek to maximize the welfare of their own country. The welfare of each country is the sum of the consumer surplus, the airline profit, and the airport profit of that country. In the first stage, each government decides which ownership type to adopt for its airport, which could be either government ownership (GO) or private ownership (PO). Under government ownership, the airport remains as a public utility and is managed by the government. Under the private ownership, the government privatizes the airport, and the resulting entity aims to maximize its own profit only. Once the airport ownership types have been selected, the two airports simultaneously set their airport charges. Consistent with the literature, we assume these charges, which are charged to the airlines, are passed onto the passengers and levied onto the airfare.7 Thus, we consider airport passenger fees, by letting Fi, i 2 {1, 2}, denote the passenger fee charged by airport i to all passengers using this airport.8 Note that each passenger needs to pay fees to both airport, F1 and F2, as the airports provide a complementary service and both need to be consumed in order to complete the trip. Given the passenger fees, in the last stage, the two airlines set their quantities, q1 and q2, as they engage in a Cournot type of competition, and demand is realized. Let pCi denote the fare paid by passengers from country i (the superscript C is for carrier). The demand for travel in country i follows a down-sloping curve with Qi = 1 Pi where Qi is the total quantity released to this market by both airlines and Pi is the full price paid by passengers for travel.9 Specifically, the full price paid by passengers of country i is the sum of the fare, pCi , and the two airport fees, F1 and F2, i.e., Pi ¼ pCi þ F 1 þ F 2 . We assume that the demand stemming from each country is for a round trip (such as is the case with passenger airlines). When demand is for round trips, demand from the two countries can be perceived as substitutable (from the airlines’ per7
Assuming exogenous load factors (see, e.g., Brueckner, 2002) airport landing fees are equivalent to airport passenger fees. In what follows,we can further study the case where a welfare-maximizing airport may employ a discriminatory pricing policy in the sense that passengers from the two different countries could be charged different fees (à la Pels and Verhoef, 2004). See also Footnote 11. 9 This simple linear demand function is adopted to avoid unnecessary complications in the analysis. The model can be generalized to a broader class of demand functions. 8
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Fig. 2. The demand in the two countries
spective), as the two demands compete for the same supply of products. Consequently, the total quantity supplied by the two airlines is shared by the demands from both countries.10 More precisely, quantity is shared by passengers from both countries to the point where prices in both markets are equal. Since the products are shared by both markets, in equilibrium, passengers from both countries pay the same fare exactly, pC1 ¼ pC2 pC . Note also, that passengers from both countries pay the same total fare Pi = P2 = pC + F1 + F2, where pC is the base airfare and F1 and F2 are the fees paid to the two airports. Thus, the demand in country i, i 2 {1, 2}, is Qi = 1 Pi = 1 Fi Fj pC. The demand from both countries is added up to yield the total demand function
Q ¼ Q i þ Q j ¼ 2ð1 ðF i þ F j Þ pC Þ;
ð1Þ
where Q = q1 + q2 is the sum of quantities set by the two airlines. We assume zero costs for the airline, so Airline i’s profit is given by PCi ¼ qi pC . Similarly, we assume zero cost for the airports, hence Airport i’s profit is given by PAi ¼ F i ðQ i þ Q j Þ. The surplus of consumers from country i is given by R Pmax i CSi ¼ P Q i ðPi ÞdPi ¼ 12 ð1 pC F i F j Þ2 ; j – i. A private airport maximizes only its own profit PAi ; i 2 f1; 2g, when setting i the passengers’ fees, while a public (government owned) airport maximizes the total welfare of the country associated with travel: W i ¼ PAi þ PCi þ CSi ; i 2 f1; 2g. The demand curves are illustrated in Fig. 2, wherein we denote by PAij the profit of airport i from passengers of country j, where i, j 2 {1, 2}. Consider, for example, the demand in Country 1. The total supply in this country is Q1 and the area under the demand curve up to this point is segmented into four components: the consumers’ surplus, the profit of Airport 1 from the passengers stemming from Country 1 PA11 , the profit of Airport 2 from the passengers stemming from Country 1 PA21 , and the airlines’ combined profit from these passengers. In the latter case one can further break down the profit between the two airlines. Note that this figure depicts a symmetric scenario. However, apart from the airfare, pC, and the total full fare paid by passengers, P1 = P2, the realizations in the two countries can differ. Specifically, the two airports may charge the passengers quite differently. 2.2. Model analysis We solve the model backward to yield the subgame perfect Nash equilibrium. We first derive the airlines’ optimal quantity decisions, then we obtain the airports’ fees to passengers for the different airport management regimes. We conclude with governments’ choice of the optimal regimes for their airports. We consider each of the airport ownership cases separately (both are government owned, both are privately owned, one is government owned and the other is privately owned). 2.2.1. Both airports are privately owned (PO–PO) Consider the case where both airports are privately owned, i.e., they set fees to maximize their respective profits. From (1) we have that pC ¼ 1 F i F j 12 ðqi þ qj Þ. Solving backward, in the final stage, the two airlines simultaneously set their quantities to maximize their profits, PCi ¼ qi pC ; i 2 f1; 2g, yielding qi ¼ 23 ð1 F i F j Þ; i – j 2 f1; 2g. Proceeding with the second stage, the two airports simultaneously maximize their profits, PAi ¼ ðq1 þ q2 ÞF i , resulting in F 1 ¼ F 2 ¼ 13. Hence, when both 2 4 2 airports are profit maximizers, we have pC ¼ 19 ; qi ¼ 29 ; PCi ¼ 81 ; PAi ¼ 27 ; CSi ¼ 81 , and W i ¼ 16 . These results are reported 81 in Table 1.
10 One can also consider the case of one way trip demand where the demand originating from each country is directional (such as cargo)—ending at the destination country. Since the airlines’ fleets operate in both directions, the total quantity supplied by both airlines is the same in each market. The insights from such a model are generally in line with the round trip assumption developed here.
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B. Mantin / Transportation Research Part B 46 (2012) 381–388 Table 1 Results for the return trip model. Cases
F1
F2
pC
qi
PCi
PA1
PA2
CSi
W1
W2
1:PO, 2:PO
1 3 1 7 1 5
1 3 3 7 1 5
1 9 1 7 1 5
2 9 2 7 2 5
2 81 2 49 2 25
4 27 4 49 4 25
4 27 12 49 4 25
2 81 2 49 2 25
16 81 8 49 8 25
16 81 16 49 8 25
1:GO, 2:PO 1:GO, 2:GO
¼ 0:197 ¼ 0:163 ¼ 0:32
¼ 0:197 ¼ 0:326 ¼ 0:32
Where PO stands for private ownership and GO for government ownership; i 2 {1, 2}.
Table 2 Welfare analysis with Cournot competition.
1:PO 1:GO
2:PO
2:GO
0.197, 0.197 0.163, 0.326
0.326, 0.163 0.32, 0.32
Where PO stands for private ownership and GO for government ownership.
2.2.2. One airport is government owned and the other is privately owned (GO–PO) Now, assume that, without loss of generality, Country 1 decides to adopt government ownership for its airport (while Country 2’s airport is privately owned). The analysis of the third stage for the GO–PO case coincides with the corresponding analysis in the case where both airports are privately owned (PO–PO). In the second stage, the airport in Country 1 seeks to maximize the welfare of the country, W1, rather than the airport profit only. Solving simultaneously, we obtain F 1 ¼ 17 and F 2 ¼ 37. Intuitively, to increase welfare, the public airport will reduce the fees charged to the passengers; however, the private airport will take advantage of this and increase its fee to passengers. Since quantity is shared to the level where total price in both countries is identical, due to demand symmetry, the only difference between the two countries stems from the airports’ 2 4 profits (i.e., consumer surplus and airline profit are the same in both countries). We have pC ¼ 17 ; qi ¼ 27 ; PCi ¼ 49 ; PA1 ¼ 49 ; 2 8 16 PA2 ¼ 12 ; CS ¼ ; W ¼ and W ¼ . The public airport (Airport 1) sets the passenger fee such that it transfers surplus 1 2 i 49 49 49 49 from the airport to the passengers. However, by doing so, it transfers surplus not only to its own local passengers, but also to the foreign passengers from the other country (Country 2).11 The other airport (Airport 2) takes advantage of this pricing by raising its own fees (and note, in Table 1, that the fees that this airport charges are higher than when both airports are privately owned). From consumers’ perspective, the former effect—the transfer of surplus from airport to passengers—dominates, as the total price decreases and their surplus improves. Yet, Country 1 suffers from a significant decrease in welfare due to the corresponding pricing by the other airport, Airport 2. The above analysis yields the following lemma. Lemma 1. Consider Cournot competition in the airline market. Assume that both airports are privately owned. A unilateral deviation from private ownership airport to government ownership by one of the countries has a detrimental effect on the welfare of the deviating country and a positive effect on the welfare of the other country. Proof. When both airports are private, the welfare of each country is 16 ¼ 0:197. If one airport is welfare maximizing and the 81 8 other is profit maximizing, their profits are 49 ¼ 0:163 and 16 ¼ 0:326, respectively. Since 0.163 < 0.197 and 0.326 > 0.197, the 49 country deviating from symmetric private airport ownership to government ownership is worse off, while the other country, which stays with a privately owned airport, is better off. h This is an important result. It reveals that if all airports were to be privatized, countries would face serious difficulties in returning to government ownership. A unilateral move from private to public ownership is not a move that improves welfare for the country that is initiating the move, hence it is not an acceptable move from a welfare perspective. Not only would it worsen the welfare of the country that changes its airport ownership type to public, it also improves the welfare of the country that stays with private ownership. Essentially, when such a move is adopted, we witness mobilization of welfare from one country (with the government owned airport) to the other (with the privately owned airport)—a concept to which we refer as welfare gravitation. 2.2.3. Both airports are privately owned (GO–GO) Lastly, if Country 2 follows suit and adopts government ownership for its airport as well, solving the model back2 4 2 8 wards,using the same stages shown above, we have F 1 ¼ F 2 ¼ 15 ; pC ¼ 15 ; qi ¼ 25 ; PCi ¼ 25 ; PAi ¼ 25 ; CSi ¼ 25 , and W i ¼ 25 . The different outcomes of the different cases are summarized in Table 1. 11 One way to mitigate this effect is to price discriminate between the passengers based on their point of origin (similar to Pels and Verhoef, 2004 who discriminate the airlines based on their origin). Surprisingly, however, such price discrimination is not welfare improving.
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B. Mantin / Transportation Research Part B 46 (2012) 381–388 Table 3 Welfare analysis in the differentiated Bertrand competition.
1:PO 1:GO
2:PO
2:GO
ð117bÞ ; ð117bÞ 9ð2bÞ2 ð1bÞ 9ð2bÞ2 ð1bÞ 4ð5bÞ ; 4ð117bÞ 9ð3bÞ2 ð1bÞ 9ð3bÞ2 ð1bÞ
4ð117bÞ ; 4ð5bÞ 9ð3bÞ2 ð1bÞ 9ð3bÞ2 ð1bÞ 5b 5b 9ð1bÞ ; 9ð1bÞ
Where PO stands for private ownership and GO for government ownership.
Even though both countries are better off in terms of welfare if they were both to adopt government ownership for their airports, they do not reach such an equilibrium, as they always have the incentive to deviate and privatize their airports. Specifically, if one country adopts government ownership for its airport, then the other country always chooses to privatize its airport. This ownership structure gravitates welfare from one country to the other and improve welfare, even if only marginally. This is summarized in the following theorem. Theorem 1. Consider Cournot competition in the airline market. The two countries find themselves in a Prisoner’s Dilemma type of inferior equilibrium with regard to the airport ownership types; even though both are better off with public (welfare maximizing) airports, they end up in the Pareto inferior Nash equilibrium where both airports are private (profit maximizers). Proof. Lemma 1 already established the fact that a deviation from the symmetric PO is not welfare improving, hence, it is a Nash equilibrium. We make use of Table 2 which summarizes the welfare outcomes in the different states. In Table 2, one can observe that from the symmetric GO a unilateral deviation by either country to PO is welfare improving. That is, the best reaction of each country is always to adopt PO. Hence, the Nash equilibrium is the symmetric PO regime. It is evident from Table 2 that symmetric PO is the Pareto inferior equilibrium and that both countries would be better off under the symmetric GO. h The focal point then is to privatize the airports even though the symmetric state where both airports are privately owned results in an inferior welfare outcome for both countries. This result suggests a ripple effect. Though we have not studied more elaborate networks of multiple countries and several airports, it appears that once a country privatizes its airport(s), others will follow along and adopt private ownership for their airports. If both airports are privately owned, welfare improvement for both countries is attained only when both adopt government ownership for their airports. Far sighted governments may realize that unilaterally deviating from the symmetric government ownership state and adopting a private ownership could ultimately be detrimental as the other country may follow suit and will adopt the same ownership type, leading both countries to experience a decrease in their welfare. Hence, such governments might consider agreements that ensure that both countries will manage their airports as public entities. However, such agreements may be interpreted as interfering with each other’s governance, and therefore are less likely to be adopted. 3. Differentiated Bertrand competition In the previous section we assumed that the airlines were engaged in a Cournot competition. Such a competition implies that the airlines are perceived by passengers as perfect substitutes, in which case airlines compete over quantities. In this section we relax this assumption and instead we assume that the two airlines are engaged in a differentiated Bertrand competition. This implies that the substitution between the two airlines is imperfect and the products are differentiated. We abstract away from airlines’ differentiation decisions as such a differentiation in our setting could stem from passengers’ preference for flying with the airline from the same country (i.e., patriotic preference as is, e.g., in Brueckner and Proost, 2010). In a differentiated Bertrand competition, airlines choose their fares and can further price fares differently for passengers based on their origin country. Let Qik and denote the round trip demand originating in Country i (to Country j) for flying with Airline k and let Pik denote the full fare paid by passengers for this trip. This full fare is composed of the airfare, pik, and the passenger fees from both airports, F1 and F2, i.e., Pik = pik + F1 + F2. The demand stemming from Country i for flying with Airline k is given by Qik = 1 Pik + bPil, b < 1, i 2 {1, 2}, k – l 2 {1, 2}.12 The first two stages are as before: in the first stage, the two countries independently choose the ownership type for their airports, and, in the second stage, each airport sets the passenger fees. In the third stage, the two airlines set their airfares and demand is realized. The analysis of the differentiated Bertrand competition is very similar to the Cournot competition model. For brevity, we do not repeat the entire analysis and we merely review the primary steps and highlight the main insights. Solving backward, in the third stage the two airlines simultaneously set their prices to maximize their respective profits, PCk ¼ p1k Q 1k þ 2 ÞþbðF 1 þF 2 Þ p2k Q 2k ; k 2 f1; 2g, yielding pik ¼ 1ðF 1 þF2b ; i; k 2 f1; 2g. 12 Note that this formulation can be easily generalized to account for possible price discrimination between the passengers based on their point of origin (by assuming different demand intercepts, own and cross price elasticities). However, here we impose symmetry to simplify the presentation and insights.
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Next, we solve the airports’ optimal passenger fees. If both airports are privately owned, then both airports simultaneously ð117bÞ 1 maximize their profits, PAi ¼ ðQ 11 þ Q 12 þ Q 21 þ Q 22 ÞF i , resulting in F 1 ¼ F 2 ¼ 3ð1bÞ , in which case W 1 ¼ W 2 ¼ 9ð2bÞ . If 2 ð1bÞ
both airports are government owned, they simultaneously seek to maximize their welfare, W i ¼ PAi þ PCi þ CSi ,13 in which 1þb 5b with W 1 ¼ W 2 ¼ 9ð1bÞ . If one airport is government owned and the other is privately owned, then the govcase F 1 ¼ F 2 ¼ 6ð1bÞ 2ð2bÞ 1þb , while the privately owned airport sets 3ð3þb , where the former country gets a ernment owned airport sets a fee of 3ð1bÞð3bÞ 2 4bÞ
welfare of
4ð5bÞ 9ð3bÞ2 ð1bÞ
and the latter obtains a welfare of
4ð117bÞ . 9ð3bÞ2 ð1bÞ
These results are summarized in Table 3.
With p symmetric government ownership, a country has an incentive to deviate and privatize its airport if ffiffiffi b > 5 2 6 0:101. From this state, the other country, whose airport is still owned by the government, always has an incentive to defect as well and privatize its airport as well. This gives rise to the following statement. pffiffiffi Theorem 2. Consider differentiated Bertrand competition in the airline market. If b > 5 2 6 0:101, then the two countries find themselves in a Prisoner’s Dilemma type of inferior equilibrium with regard to the airport ownership type; though both are better off with public (welfare maximizing) airports, they both employ the pffiffiffi unique Pareto inferior Nash equilibrium where both airports are privately owned (profit maximizers); otherwise, if b < 5 2 6 0:101, then there exist two subgame perfect Nash equilibria: either both privatize their airports or both keep them as public utilities.
Proof. It follows from Table 3: a unilateral deviation by, say Country 1, from {PO, PO} to {GO, PO} is never beneficial, since 4ð5bÞ > 9ð3bÞ , so {PO, PO} is a candidate for NE. Since a unilateral deviation by, say Country 1, from {GO, GO} to {PO, 2 ð1bÞ pffiffiffi pffiffiffi 4ð117bÞ 5b > 9ð1bÞ ) b > ð5 2 6Þ, {PO, PO} is the unique Nash equilibrium if b > 5 2 6, otherGO} is beneficial only if 9ð3bÞ 2 ð1bÞ
ð117bÞ 9ð2bÞ2 ð1bÞ
wise, both {PO, PO} and {GO, PO} are Nash equilibria. It is evident that {GO, GO} is preferred by both over {PO, PO} since 5b 9ð1bÞ
ð117bÞ > 9ð2bÞ always holds true, establishing that {PO, PO} is the inferior Pareto equilibrium in this scenario. 2 ð1bÞ
h
To gain insight into this result, first consider the equilibrium state, which is symmetric private ownership. If one of the countries unilaterally deviates to government ownership for its airport, it reduces the passenger fees while the other airport, which is privately owned, takes advantage of this pricing decision and increases its own fees (yet, the sum of the fees drops). The difference in passenger fees results from welfare gravitation from one country to the other. With this deviation (of one airport from PO to GO), the base airfare increases, yet the full airfare decreases (as the decrease in passenger fees dominates the increase in airfare), so consumers are better off. As the airfare increases, despite the decrease in full airfare, the airlines’ profits increase. Lastly, due to the decrease in fees, the profit of the GO airport is lower than under the symmetric PO state. This decrease is so substantial that it dominates the combined increase in consumer surplus and the airline’s profit, implying that a deviation from symmetric PO state is not beneficial to either country. Now, consider the symmetric government ownership. If one country unilaterally deviates to PO, it raises the passenger fees, taking advantage of the decrease in fees at the GO airport (yet, the sum of passenger fees decreases). The base fare decreases, yet the total fare increases, resulting in a decrease in airlines’ profits. The deviating country (now with PO airport) experiences an increase in airport profit. When b is sufficiently high (i.e., substitution is high) the increase in airport profit dominates the decrease in consumer surplus and the airline’s profit. Hence, a defection from the symmetric GO occurs, facilitating a corresponding move by the other country, ultimately resulting with the symmetric PO equilibrium. 4. Concluding remarks This work contributes to the limited literature that considers airport complementarity, contrasted with the widespread modeling approach where airports are studied independently. Particularly, we are interested in the decision process—modeled as a game theoretic process—of privatizing airports vs. keeping them as public entities under government ownership. In the absence of airport complementarity, a publicly owned airport naturally yields welfare maximization. Here, we showed that when two airports provide a complementary service, each in a different country, publicly owned airports do not necessarily result in welfare maximization. Specifically, the best option for each country to take is to privatize its airport (except when cross price elasticities are low, when the airlines are engaged in a differentiated Bertrand competition). Indeed, if both airports are publicly owned, both countries could be better off in terms of welfare. Yet, the unique subgame perfect Nash equilibrium is the state where both countries privatize their airports, which is a Pareto inferior equilibrium. This result has been shown to be robust as it holds both for Cournot competition and differentiated Bertrand competition (except when cross price elasticities are low, in which case there exists two symmetric Nash equilibria). This work has explored the importance of the inclusion of complementarity effects on airport ownership modes. This aspect shall play a major role in considering and evaluating bilateral and multilateral agreements. For example, the results of 13
In this differentiated Bertrand competition model, consumer surplus in Country i is is the vector of prices.
P R max pik k
pik
Q ik ðpÞdp ¼
P
1 k 2 ð1
þ bpil pik Þð1 pik þ bpil Þ; l – k, where p
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this paper are very important for the issue of open skies, as most European airports are, or are being, privatized, while in the US they are publicly owned. This work can be extended in many important ways. For example, larger networks can be considered where additional airports exist. Such airports could be hubs (or gateways) or end nodes connecting to the hubs. In such a scenario, the decision space expands dramatically as a country may choose to privatize some of its airports while keeping the remaining airports as public entities. When accounting for larger networks, one can also consider more than two countries. However, such a generalization is expected to amplify the results of this work, as the adoption of government ownership for an airport, while all others are under private ownership, may result in welfare gravitation to more than one country. Importantly, one can also consider another regulatory decision: whether to let the two competing airlines merge (or collaborate) and act as a monopoly in this market. Lastly, we have abstracted away from airport concession income.14 Modeling such non-aeronautical income is challenging in the presence of multiple airports: can it be consumed at any of the airports (in which case the airports compete over this service) or can it be consumed only at one end of the trip (such as car rental, and in this case the service is complementary). Acknowledgments The author thanks David Gillen for his valuable feedback and Lorra Ward. This research was supported by a Natural Sciences and Engineering Research Council of Canada (NSERC) grant and by the Transport Canada support for research under the Asia–Pacific Gateway and Corridor Initiative provided by the Center for Transportation Studies at the University of British Columbia. The author is also grateful for the constructive feedback provided by the two referees, which has significantly improved the paper. References Basso, Leonardo, 2008. Airport deregulation: effects on pricing and capacity. International Journal of Industrial Organization 26 (4), 1015–1031. Basso, Leonardo, Zhang, Anming, 2007. An interpretative survey of analytical models of airport pricing. In: Lee, Daren (Ed.), Advances in Airline Economics, vol. 2. Elsevier Publishers, Netherland. Brueckner, Jan K., 2002. Airport congestion when carriers have market power. American Economic Review 92 (5), 1357–1375. Brueckner, Jan K., 2005. Internalization of airport congestion: a network analysis. International Journal of Industrial Organization 23 (7–8), 599–614. Brueckner, Jan K., Proost, Stef, 2010. Carve-outs under airline antitrust immunity. International Journal of Industrial Organization 28 (6), 657–668. Czerny, Achim I., 2006. Price-cap regulation of airports: single-till versus dual-till. 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14 Studying airports’ concession income is gaining increasing attention. Due to the complementarity between airside and commercial revenues airports may have less incentive to abuse their power. See, e.g., the works by Starkie (2001), Morrison (2009), and Zhang and Zhang (2010).