Journal of Air Transport Management 15 (2009) 195–203 Contents lists available at ScienceDirect Journal of Air Transport Management journal homepage: www. elsevier. com/locate/jairtraman Pricing strategies of low-cost airlines: The Ryanair case study Paolo Malighetti a, *, Stefano Paleari a, Renato Redondi b a b Department of Economics and Technology Management, University of Bergamo– Universoft, Viale Marconi 5, Dalmine 24044, Italy Department of Mechanical Engineering, University of Brescia – Universoft, Via Branze, 38 – 25123 Brescia, Italy a b s t r a c t Keywords: Dynamic pricing Low-cost Ryanair Fares

We analyse the pricing policy adopted by Ryanair, the main low-cost carrier in Europe. Based on a year’s fare data for all of Ryanair’s European ? ights, using a family of hyperbolic price functions, the optimal pricing curve for each route is estimated. The analysis shows a positive correlation between the average fare for each route and its length, the frequency of ? ights operating on that route, and the percentage of fully booked ? ights. As the share of seats offered by the carrier at the departure and destination airports increases, fares tend to decrease. The correlation of dynamic pricing to route length and the frequency of ? ghts is negative. Conversely, as competition increases discounts on advance fares rise. O 2008 Elsevier Ltd. All rights reserved. 1. Introduction In recent years, the entry of low-cost carriers has totally revolutionised the air passenger transport industry. The low-cost business model was introduced by Southwest in the US at the beginning of the 1970s. However, it was only in the 1990s that the phenomenon spread worldwide. Ryanair was one of the ? rst airlines in Europe to adopt the low-cost model in 1992. Easyjet, Ryanair’s main low-cost competitor, was founded in 1995.

Although the phenomenon is relatively recent, the stunning results obtained by low-cost carriers urge academics to study the reasons for their success. The reduction of costs lies at the core of the low-cost business model, which aims to offer lower fares, eliminating some comfort and services that were traditionally guaranteed (hence the de? nition of ‘‘no frills’’, often employed to refer to low-cost ? ights). The use of an on-line booking system, the suppression of free in-? ight catering, the use of secondary airports connected through a pointto-point network, and the use of homogeneous ? ets are only a part of the innovative choices made by low-cost airlines. Many studies have analysed low-cost businesses, highlighting the keys to lower costs (Alamdari and Fagan, 2005; Doganis, 2006; Franke, 2004), and the role played by entreprership (Cassia et al. , 2006). The containment of costs is only one of the reasons for the success of a low-cost carrier. Alertness to ‘‘latent demand,’’ characterised by the passenger’s willingness to pay elastic prices, which is not the attitude of the so-called ‘‘traditional’’ passenger, is among the key factors. In the airline business, the maximisation of the pro? s obtained from each ? ight is strictly related to the maximisation of revenues, because many of the costs incurred are essentially ? xed, at least in the short term. Pricing has always represented an important factor in the carriers’ choices, driving the adoption of different strategies by low-cost and full-cost carriers. Full-cost carriers choose price discrimination techniques based on different fare classes, complex systems of discounts with limited access, customer loyalty schemes, and overbooking techniques. Low-cost carriers instead use ‘‘dynamic pricing’’.

Because of dynamic pricing, it is now common for people to buy air tickets to European destinations for less than V10. 00 (airport taxes excluded). This paper deals with the pricing policies of low-cost carriers, offering a detailed analysis of Ryanair, the main developer of the low-cost model in Europe. Generally speaking, fares tend to increase until the very last moment before the closing of bookings. If it is assumed that Ryanair aims to maximise its pro? ts, it is to be expected that travellers are prepared to bear higher costs more easily as the date of ? ight approaches.

We aim to identify the competitive and contextual factors that drive the choice of the average fares, and their relative dynamics. In details, our analysis will focus on Ryanair’s pricing policies in correlation with the features of its airport network. The results show that the fare policy is clearly innovative relative to traditional pricing strategies, and that the fares are in? uenced by the competitive economic context in which the route is offered. 2. State of the art This study refers to two main ? elds of literature, namely the analysis of the low-cost business model and the study of dynamic pricing techniques.

The main point of interest is the extraordinary * Corresponding author. E-mail address: paolo. [email protected] it (P. Malighetti). 0969-6997/$ – see front matter O 2008 Elsevier Ltd. All rights reserved. doi:10. 1016/j. jairtraman. 2008. 09. 017 196 P. Malighetti et al. / Journal of Air Transport Management 15 (2009) 195–203 performance of the major low-cost carriers, especially when compared with the trend, and the average pro? tability, of the air transport industry in general. Researchers have extensively examined the cost-effective policy, which so clearly permeates the lowcost business model.

Franke (2004) and Doganis (2006) have focused in particular on the cost bene? ts that low-cost carriers can derive from their operational choices. Their studies show that there is no single driving element responsible for the competitive advantage. Rather, all the choices made contribute to the production of cost bene? ts. Gudmundsson (2004), using a longitudinal survey approach, studies factors explaining the success probability of the ‘‘new’’ airlines and ? nds that productivity and brand image focus are signi? cantly related to ? nancial non-distress, whilst market power (market-share) focus is signi? antly related to ? nancial distress. A ? rst mover competitive advantage could explain why the most successful airlines seem to be able to maintain their market leadership in the short and medium term, are the ones that gave rise to the phenomenon, as witnessed by the likes of Southwest in the USA and by Ryanair and Easyjet in Europe. It is clear that, a good lowcost strategy can never be replicated in all its detailsdand this could account for the carriers that succeeded as well as for those that did not. Alamdari and Fagan’s (2005) study quanti? d the impact of the deviation from the original low-cost business model. The importance of the different strategic choices made by carriers suggests investigating other elements of the low-cost business model. Revenue analysis is an important element that has been less studied. Indeed, the generation of revenues is one distinctive aspect differentiating low-cost from full-cost airlines policies. Piga and Filippi (2002) have analysed the pricing policies of the low-cost business model in comparison with the pricing strategies of the full-cost airlines.

Coherent choices seem to be essential in pricing policies as well. For instance, the widespread use of the Internet for the sale of tickets tends to decrease price dispersion. This phenomenon may in part be attributed to the ‘‘ef? ciency of electronic markets,’’ as de? ned by Smith (Smith et al. , 2000). The success of the low-cost model is based on a fragile balance between fare levels, load factors and operating costs. The structure of revenues and the determination of prices are nearly as important as the minimisation of costs in the equation of pro? ts.

Indeed, an excellent pricing strategy for perishable assets results in a turnover increase, ceteris paribus, which can be quanti? ed between 2% and 5%, according to Zhao and Zheng’s (2000) study. The analysis of fare levels and policies aims to understand the key factors in the achievements of low-cost carriers, including the effects of the competitive interaction between carriers (Pels and Rietveld, 2004). The price choices and the ability of the airlines to understand the characteristics of the demand, in either a condition of monopoly or a competitive context, are decisive in the balance of the business model itself.

Fare dynamics must be taken into account in a thorough evaluation of market competitiveness, and of the bene? ts travellers have achieved through deregulation. This paper analyses the pricing strategies adopted by Ryanair against the characteristics of the context in which it operates, including the degree of competitiveness. First, the study deals with the demand curve derived from Ryanair’s prices. The analysis starts from the microeconomic principles of dynamic pricing. Generally speaking, airlines deal with perishable goods sold in different time steps, ith the aim to maximise pro? ts. The offer of seats on a ? ight can be compared to the sale of ‘‘perishable assets’’ with pre-determined capacity in conditions of negligible marginal costs. The themes investigated by the relevant literature are dynamic pricing and yield management. Zhao and Zheng (2000) have determined the minimum conditions required for optimal dynamic pricing. Because the price trend is in? uenced by demand, one part of the literature focuses on optimal pricing policies by using speci? c functional forms to represent demand and customer bene? ts.

For example, it is quite typical to use an exponential demand curve (Gallego and Van Ryzin, 1994) and a mechanism ‘‘of customer arrival’’ into the market with a probability similar to a Poisson process. The studies mentioned above presuppose a continuous optimal price function. Other studies are more likely to hypothesise the existence of a limited range of prices (Wilson, 1988). The present study adopts a continuous function, because Ryanair offers a wide range of prices. The study of price dynamics raises interesting questions. Many travellers have probably noticed that prices often tend to increase as the ? ght date approaches. According to McAfee and te Velde (2006), in the period preceding the ? ight date, the price trend mainly depends on the trade off between the option of waiting for a potential lower price, and the risk of seats becoming unavailable. In this case, the functional form of the demand curve, together with its adjustment over time, also help to determine a series of minimum prices. This study analyses the range of actual prices on all of Ryanair’s routes. It aims to validate some of the assumptions made in the literature through a thorough study of this wide empirical sample.

The estimated demand curve makes it possible to make inferences about the trend of bookings and the curve relating to the fully booked aircraft. Stokey’s (1979) studies determined an optimal constant ? lling curve in a context of monopoly. Similar results can be obtained by using a demand with functional forms belonging to the family of continuous functions presented by Anjos et al. (2005). For such functions, when dealing with goods that are to be sold by a given deadline, it is possible to de? ne and implement the optimal pricing strategy.

The reference curves adopted in this study belong to the Anjos family of curves. The structure of demand, which guides the optimisation choices of the carrier, is in? uenced by the presence of competitors, and the passengers’ opportunities to opt for a substitute service. Classical studies, starting from Borenstein’s (1989) analysis, have mainly focused on the airlines’ average fare level, showing the undeniable in? uence exercised by the competitive structure on the fares of fullcost airlines. Such competitive structures are exempli? ed by a fare premium correlated to the dominance of the hub of reference.

Alderighi et al. (2004) have pointed out that full-cost airlines tend to decrease fares on routes also operated by low-cost carriers. The in? uence of the competitive structure on the pricing strategies of low-cost carriers has been less studied, as far as we know. Pels and Rietveld’s (2004) studies have examined the evolution of fares on the London–Paris route; traditional behavioural models do not seem to apply here, given the mixture of direct and indirect competition. It is not clear whether the presence of other airlines can critically affect the pricing strategies of low-cost carriers. Pit? ld (2005) has analysed the routes originating from Nottingham East Midlands airport in 2003, when it was possible to observe low-cost airlines in direct competition. The results showed a weak in? uence of the competitive structure on prices. The historical pattern of fares offered by each airline seems to play a more important role, as would be expected in a situation of price leadership. In a study examining the London–Berlin and London–Amsterdam routes, Barbot (2005) found that the low-cost and full-cost markets coexist on totally separate levels, so that low-cost carriers compete ‘‘only’’ among themselves, as do full-cost carriers.

The approach we have adopted here focuses on the different behaviours assumed by carriers according to the distinctive characteristics of the routes they operate. We aim to identify the competitive and contextual factors that drive the choice of the average fares, and their relative dynamics. P. Malighetti et al. / Journal of Air Transport Management 15 (2009) 195–203 197 3. Methodological aspects The literature on low-cost carriers highlights the important role played by dynamic pricing. It is assumed that once the ? ights have been scheduled, the marginal costs incurred in relation to the number of passengers are practically null.

It follows that the maximisation of pro? ts is strictly dependent on the maximisation of the revenue function. Let the reference unit of time be the single day. 1 Considering T days, the revenue R can be expressed as This study considers the functional form of demand as proposed by Anjos et al. (2005), where the demand for air tickets depends on price levels, and on the time interval between the purchase date and the ? ight date, according to qi ? AeAa$pi F? i? where i?? 1; K; T? (6) R ? T X i? 1 pi qi (1) where pi is the ? ight price on the day i of the year, and qi is the number of seats booked on the same day.

The optimal pricing strategy results from the maximisation of the previous expression, under the binding limit of the aircraft’s capacity, which can be expressed as T X i? 1 where A and a are two constants, and F(i) is a function positively correlated to the time period between the purchase date and the ? ight date. In this case, the function of demand is subject to an exponential decrease as the advance purchasing time increases. An advance booking is less useful because people are less sure of their plans far in advance. Given the functional form of the demand in expression (6), it is possible to identify the optimal ricing strategy by substituting the following form for pi in expression (5). pi ? m ? 1 a$F? i? (7) qi Q (2) where Q is the capacity, that is, the total number of seats available on the aircraft. For the purposes of this study it is assumed that, for the speci? c route and type of customers availing themselves of low-cost ? ights, the operator is not a price-taker. We hypothesise that the competitive structure and the level of market and product differentiation enable the operators to modify the price variable. The maximisation problem can be solved through a ‘‘lagrangian’’.

The multiplier m can be viewed as the extra charge assigned to the fully booked ? ights. 2 In the next section, some F(i) forms will be tested on Ryanair’s actual prices. The parameters of the price function will be estimated by minimising the quadratic error compared to the actual prices. The underlying assumption is that Ryanair operates by maximising its revenues, and using a demand function similar to function (6). Therefore, the accuracy that may be obtained using the model for the estimation of prices enables assessment of the validity of the forms of the demand curves.

Through the substitution of the optimal price expression (7) in the expression (6), we have L ? T X i? 1 pi qi ? m Q A T X i? 1 ! qi (3) qi ? AeA1 (8) where m represents the Kuhn–Tucker’s multiplier, which takes into account the aircraft limit of capacity. It follows that m QA T X i? 1 ! qi ? 0 Expression (8) implies that, following the application of the optimal price, the expected demand is steady over time. If the quantity sold over a certain time span is greater than the steady expected quantity, the operator may decide to raise the price.

Similarly, the operator may decide to reduce the price in order to gain demand when demand is scarce. In the empirical calculations, two functions are used for the estimation of prices. The ? rst expression is If the limit of capacity is reached, m > 0; if not, m ? 0. In order to determine the optimal price pi at the speci? c time i, the derivative of the expression (3) with respect to pi must equal zero, thus obtaining T vq X vL j pj A m ? qi ? ? 0 vpi vpi j? 1 pi ? m ? 1 a$? 1 ? b$i? (9) where i?? 1; K; T? (4) This expression can be held valid even if the markets on the different days are not ‘‘separated. ’ In this case, for example, the fare during one period can modify the quantity of available seats in a successive period, that is, vqj/vpi s 0 with i s j. In line with many of the studies analysed in the literature, for the purpose of this study, it is assumed that the markets for the purchase of air tickets are separated in time, that is vqj/vpi ? 0 with i s j. A later development of this study will eliminate this hypothesis in order to verify the possible interaction between the demands of the different periods. Here, expression (4) is simpli? ed in the following optimal conditions: here i is the number of days between the advance reservation and the ? ight date. The form of the optimal price is a hyperbola with the price going up as the ? ight date approaches. This functional form makes it impossible to obtain price reductions as the ? ight date approaches. A more complete functional form is pi ? m ? 1 p? a$ 1 ? b$i ? g$i2 ? q i (10) vq qi ? ?pi A m? i ? 0 vpi where i?? 1; K; T? (5) In this case, the price may decrease as the departure date approaches. The degree of accuracy of both functional forms will be discussed in the next section. The hypothesis is that Ryanair has tailored a pricing strategy for speci? routes. In other words, it is assumed that Ryanair holds speci? c values for the parameters in (9) and (10) for each individual route. An estimation of the parameters of the price functions is made for each route using data from the 90-day period before the ? ight date. 1 Demand and prices are assumed to be ? xed over the single day. 2 Fully booked ? ights have no available seats on the day before departure. 198 P. Malighetti et al. / Journal of Air Transport Management 15 (2009) 195–203 Table 1 Variation of the network operated by Ryanair between July 2005, and June 2006.

Variable Number of served airports Number of daily ? ights (average) Number of routes Percentage of routes with daily ? ight frequency Percentage of routes with more than a daily ? ight frequency Percentage of routes with no daily ? ight frequency 7/1/2005 95 650. 2 442 70. 1% 23. 6% 6. 3% 6/30/2006 111 820. 7 594 70. 8% 3. 4% 25. 8% 4. Sample and descriptive analysis 4. 1. Reference data Our database includes the daily fare for each route3 operated by Ryanair over the 4 months prior to the ? ight. The study examined all the ? ights scheduled by Ryanair from 1st July, 2005, until 30th June, 2006.

The database enables (1) a comparison between the fares for the different routes, and (2) tracing the fare variation for each individual route as the ? ight date approaches. 4. 2. Characteristics and evolution of the network operated by Ryanair Ryanair’s network is characterised by a very dynamic and steady expansion. A comparison between the data gathered as of 1st July, 2005, and later on 30th June, 2006, gives a clear picture of the dimensions of the phenomenon: in July, 2005, Ryanair served 95 airports, increasing to 111 one year later; over the same period, routes expanded by 34. %, reaching the total number of 594 (see Table 1). Nonetheless, 25 routes that were operated in July 2005 were then cancelled; 6 routes saw their ? ight frequency halved; and the frequencies of 16 other routes were each decreased by more than 10%. Ryanair operates on many low-frequency routes, 70. 8% of the overall network being made up of routes with only one single ? ight per day. By and large, it may be said that Ryanair serves its routes daily. However, in 2005–2006 this trend changed, as the number of routes with no guaranteed daily ? ight increased from 14 to 77.

An estimation of Ryanair’s ASK4 (Available Seat Kilometres) distribution is made possible by the information available about the scheduled ? ights, and the distance between the departure and arrival airports. From a geographical point of view (see Fig. 1), Ryanair’s main business focuses on the connection between England, Ireland, and the rest of Europe (44. 2% of the routes, and 49% of the ? ights start at British or Irish airports). The major ? ow (measured in ASK) is between Italy and England (14. 6%) (see Table 2). Apart from the British Isles, the main ? ow is between Italy and Spain (3. 1% of the whole business).

The domestic routes play a relatively small role, accounting for less than 5% of the scheduled air traf? c, in terms of numbers of both ? ights and routes. Italy is the only place besides the British Isles in which Ryanair operates domestic routes. The signi? cant increase in new routes and markets occurred in a surprisingly balanced way. The geographic distribution in 2006 is approximately the same as in 2005, with only a slight decrease in service to the UK (Table 3). Ryanair’s network comprises mainly short-length journeys, with all its routes ranging between 200 km and 2000 km and with a median value of 1040 km (as shown in Fig. ). The distribution proves symmetrical with respect to the median value, forming a bell-shape histogram with the exception of two peak levels at 450 and 1800 km. Fig. 3 shows the percentile distribution of ticket prices with respect to advance booking in days. It is understood that prices may vary according to other parameters as well, for example, route speci? city. Yet the role played by advance reservation in Ryanair’s pricing policy is so signi? cant that average ? gures also provide important information about Ryanair’s pricing strategies. For D% 16. 8 26. 2 34. 4 instance, the ? ures demonstrate that in 75% of cases (75th percentile in Fig. 3) the price5 does not exceed V50 for bookings made at least 20 days earlier than the actual date of ? ight. On the contrary, during the last week prior to the ? ight all prices increased sharply, with ticket prices exceeding V75 within 3 days of the date of ? ight in 50% of the cases, and topping V200 in 5% of the cases. The impression of a steady increase in prices as the date of ? ight approaches is veri? ed only on average. As a matter of fact, Ryanair makes sure to provide ‘‘special offer’’ periods in which fares reach their lowest.

Such periods do not seem to have any particular recurrence in terms of length and time. When restricting the analysis to ? ights operated on the same route only, it is not possible to mark a speci? c period for promotions. Indeed, most routes show a slight increase in prices, or at least a steady upward trend similar to most of the percentiles shown in Fig. 3. Fig. 4 shows the average price trend on the Rome Ciampino–London Stansted route (one with high-frequency service), while Fig. 5 shows the exact price on speci? c dates. Fig. compares two price trends pertaining to two dates, neither of which falls on a holiday (such as a bank holiday or a religious festival). No steady price trend can be observed in either case: over the 90 days leading to the ? ight date, lower fares are offered as the departure day approaches, but this occurs in the two cases during different periods of time, with different lengths and intensities. If it is assumed that this phenomenon may occur often in Ryanair’s pricing policy, it may be inferred that the expectations of the passengers should admit a probability (p) for the price to fall in the ollowing days. Thanks to the database at our disposal, we were able to investigate the recurrence of special offers in Ryanair’s pricing policy. For each individual ? ight we calculated the percentage of days on which the price offered was lower than any other previous price. Data were gathered per route, and analysed according to the pattern of distribution of the percentages. Fig. 6 shows the distribution by percentiles on the Rome Ciampino–London Stansted route. On this route, 50%6 of the ? ights monitored (‘50th percentile’ in Fig. ), do not show any downward price trend within 30 days of the date of ? ight. In the case of 30-day advance bookings, 25% of cases (75th percentile curve) were recorded with at least 6 following days on which prices were lower than the one recorded on the day, whilst 2. 5% of cases recorded at least 18 days in a row with lower prices. The data gathered do not provide information about the actual number of seats booked for each single ? ight. Conclusions on volumes are drawn in the empirical analysis (Fig. 10). Nevertheless, the data show whether the ? ghts were fully booked in the 24-h period before the scheduled departure date. As a matter of fact, Ryanair makes use of a non-refundable ticket policy and no 3 At the beginning of July 2005, the total number of routes was 442, while by the beginning of July, 2006, it had risen to 594. The de? nition of route is to be intended here as directional. Outbound and inbound routes between two airports are thus considered as two different routes. 4 ASK (Available Seat kilometres) accounts for the number of seats available on a ? ight multiplied by the route’s length (in kilometres). Unless otherwise stated, the price mentioned throughout this work refers to the ‘‘net’’ fare indicated on Ryanair’s website, which excludes other cost categories such as airport taxes, security fees and credit/debit card handling fees. 6 Referred to 691 out of 1382 ? ights monitored on the route analysed. P. Malighetti et al. / Journal of Air Transport Management 15 (2009) 195–203 199 Table 3 Distribution of Ryanair’s ? ights considering their country of origin and their variation. Situation as of 1/7/2005 Routes AT BE CZ DE DK ES FI FR HU IE IE (domestic) IT IT (domestic).

LT LV NL NO PL PT SE SK UK UK (domestic) Fig. 1. Distribution of Ryanair’s ? ights and served airports (as of 30th June, 2006). Total 5 11 1 41 2 52 3 30 – 50 69 (6) – 4 5 5 1 3 17 – 143 (10) 442 Daily ? ights (average) 6. 0 16. 6 1. 0 50. 6 2. 7 65. 3 3. 0 40. 1 – 91. 8 94. 4 (10. 0) – 4. 0 5. 7 6. 3 1. 0 4. 0 23. 0 – 234. 8 (21. 5) 650. 2 Flight share 0. 9% 2. 6% 0. 2% 7. 8% 0. 4% 10. 1% 0. 5% 6. 2% – 14. 1% 14. 5% (1. 5%) – 0. 6% 0. 9% 1. 0% 0. 2% 0. 6% 3. 5% – 36. 1% (3. 3%) 100% Situation as of 6/30/2006 Routes 5 16 1 48 2 61 3 46 1 80 (2) 78 (6) 3 6 6 7 18 7 20 4 183 (14) 594 Flights (average) 6. 0 21. 1. 0 61. 5 2. 9 75. 1 3. 4 55. 3 1. 0 123. 7 (6. 0) 108. 0 (12. 0) 3. 0 6. 6 6. 7 8. 3 19. 4 8. 0 26. 0 5. 0 278. 1 (25. 4) 820. 7 Flight share 0. 7% 2. 6% 0. 1% 7. 5% 0. 3% 9. 2% 0. 4% 6. 7% 0. 1% 15. 0% (0. 7%) 13. 2% (1. 5%) 0. 4% 0. 8% 0. 8% 1. 0% 2. 4% 1. 0% 3. 2% 0. 6% 33. 9% (3. 1%) 100% overbooking procedures, which means that when a ? ight is fully booked the website shows the unavailability of seats. For each individual ? ight, we calculated the fully booked ? ight ratio (where fully booked ? ights are de? ned for our purposes as those with no available seats in the last 24 h before departure).

Fig. 7 shows the distribution of routes according to the fully booked ? ights ratio. The same period was monitored for all routes and covered all of the months considered in the analysis. The ? gures highlight the unquestionable ability to ? ll all seats available on the different routes, with most of Ryanair’s routes being declared fully booked 10–20 times out of 100. 5. Empirical analysis In the empirical analysis, we applied Eq. (9) to estimate the price trends for each individual route. The equation was obtained from an exponential demand function subject to Ryanair’s pro? maximisation, and showed that, as the date of ? ight approaches, the price trend tends to resemble a hyperbola driven by parameters a and b, where a indicates the highest price level that may be reached during the last days before the scheduled departure date. The lower a is, the higher the fare will be the day before departure. Parameter b indicates instead a decrease in the fares that is directly proportional to the increase in the number of advance booking days before departure. A low b will show a steady price trend as the number of advance booking days increases. On the contrary, a high b indicates a signi? antly discounted fare, with respect to the highest fare ever offered, on advance purchases. Finally, parameter m shows the average surcharge in the cases of ? ights characteristically fully booked on the day before the scheduled departure. These parameters were calculated for all routes for which fares dating back to at least three months before the actual date of ? ight were available. 550 out of the 594 monitored routes have been taken into consideration. The remaining routes had been only recently introduced, were monitored for less than three months, and consequently were not taken into account.

The parameter estimates were carried out by minimising the standard error of the predicted fares for each individual route. Table 2 Main ? ows between nations operated by Ryanair (as of 30th June, 2006). Rank 1 2 3 4 5 6 7 8 9 10 Country pairs England – Italy England – Spain England – Ireland England – France England – Sweden England – Poland England – Germany Ireland- Spain Italy – Spain Italy – Germany ASK (daily average) 22,301,303 19,538,299 11,175,029 10,620,722 6,754,428 6,160,721 5,353,365 5,228,941 4,796,374 4,680,690 % 14. 6 12. 8 7. 3 6. 9 4. 4 4. 0 3. 3. 4 3. 1 3. 1 Fig. 2. Route distribution according to route length (as of 1st July, 2006). 200 P. Malighetti et al. / Journal of Air Transport Management 15 (2009) 195–203 Fig. 5. Prices on the Rome Ciampino–London Stansted route for two speci? c dates. Fig. 3. Fares trend distribution according to advance booking in days. The distributions of parameters a and b are shown in Figs. 8 and 9 respectively. The distribution of parameter a shows a higher frequency of routes with parameter a levels around 0. 008–0. 01, with a maximum average price higher than V100.

Parameter b shows the maximum relative frequency with levels slightly above zero; the frequency then decreases as parameter b gets higher. Some routes show a signi? cant higher b level: approximately 50% of the routes register a b level greater than 0. 1. In these cases, the purchase of the ticket three months before departure captures a price less than one tenth of the highest fare, which may occur just a few days before the date of ? ight. The pattern of distribution of parameter b suggests the presence of a cluster of routes characterised by very different dynamic pricing intensity.

Yet tests carried out by gathering routes according to the potential presence of competitors do not highlight any signi? cant differences among the clusters. It is important to note that routes in competition with one another are characterised by speci? c features, such as a high concentration of service areas with a high GDP (Gross Domestic Product). For this reason, we use regression models to help isolate the effects of each individual variable. After obtaining the parameters of the optimum price demand curve, it is possible to estimate the average number of daily bookings for each individual route using Eqs. 6) and (8). Fig. 10 shows, for the high-frequency Rome Ciampino–London Stansted route, the average ticket price, the estimated price as calculated with Eq. (9), and on the far right, the estimated number of daily bookings. Thanks to the optimal pricing strategy employed, the number of daily bookings remains steady as the date of ? ight approaches, in accord with Stokey’s (1979) study. A series of reasons may explain why the estimated and the actual price do not perfectly overlap. First of all, the demand curve cannot be accurately known on a daily basis, and there may be more or fewer bookings than expected on some days.

If the actual bookings outnumber expectations, carriers are likely to raise prices in order to deter further bookings, and thus restore the optimum situation. Secondly, operational reasons make Ryanair’s fares subject to a discrete rather than constant variation, so that Ryanair’s decision to raise its fares results in increases through small increments (generally V5. 00). Finally, the parameters were predicted by considering every single ? ight on every single route, with the aim to provide an extensive amount of data. Nevertheless, it is most likely that both time of the day and day of the week signi? antly affect pricing strategies. Thanks to the broad database at our disposal, it will be possible with a future development of the analysis to estimate these parameters according to day of the week and time of the day as well. Following the estimation of the price curve levels and the ‘‘? ight-? lling’’ function for each route, a regression analysis has been carried out, aiming to study the possible determinants in Ryanair’s pricing strategies. The ? rst regression analyses the ‘‘temporal’’ average price as a dependent variable.

This is the arithmetic mean of prices offered on a speci? c route over a period from three months prior to departure up to the day before. If the ? ight-? lling curve proves optimal, which means that the expected number of average daily bookings is steady over time (Stokey, 1979), the weighted price average against the total number of purchased tickets will equal the temporal average price. The explanatory variables employed are basically of two kinds: route speci? c variables, and airports and linked areas speci? c variables. The route speci? variables include route length and daily frequency, percentage of fully booked ? ights, number of carriers in Fig. 4. Average price trend on the Rome Ciampino–London Stansted route according to different daily departure times. Fig. 6. Percentage of remaining booking days with fares lower than the price applied on the speci? c date. P. Malighetti et al. / Journal of Air Transport Management 15 (2009) 195–203 201 Fig. 7. Distribution of number of routes by fully booked ? ights percentage. Fig. 9. Distribution of the number of routes according to coef? cients b estimated by analysing ? ght fares. direct competition on the route, and the overall taxation level to which ticket fares are subject. Information about the GDP generated by the areas connected and their population density may instead be ranked among the airport and hinterland areas speci? c variables. In addition, two other variables were put into place in order to reckon Ryanair’s importance in the departure and arrival airports: Ryanair ASK/ Departure ASK and Ryanair ASK/Destination ASK. Such variables were calculated as the ratio between the total ASK provided by Ryanair on a speci? route and the total ASK provided by the departure and destination airports. The results of the regression analysis are shown in Table 4. The most signi? cant variable affecting the average price for each route is quite predictably the route length. Of similar importance are the variables referring to demand, such as route frequency and percentage of fully booked ? ights, which show positive coef? cients. This con? rms that the higher the demand (both in terms of percentage of fully booked ? ights and daily route frequency), the higher the average prices.

Regarding the variables conveying Ryanair’s importance in the departure and destination airports, it is interesting that, on average, the greater the importance of Ryanair, for example in its role as main connecting carrier of minor airports, the lower will be the fare. The offer of the discounted fares appears as an incentive to use secondary airports. Moreover, the price correlated positively with the population density of the destination airport. An interpretation of the variables concerning the GDP of the areas connected proves more dif? cult.

The results seem to outline a strategy that fosters demand in high GDP areas. It follows that Ryanair’s strategy is keen to attract the latent demand for extra ? ights typical of the middle class, which is particularly concentrated in high GDP areas. Middle class passengers may be prepared to spend their money on leisure trips, while still being quite sensitive to price changes. A positive correlation was also found between Ryanair’s average price and the overall taxation level on the route, which incidentally could be seen as a proxy variable of the service level provided by the airport.

Finally, the presence of competitors does not seem to heavily impact the average price, which con? rms once more the complexity and diversity of forms that characterise competitiveness in the air transport industry. As we will see in the following pages, the analysis suggests that it is rather the dynamic pricing that is more likely to be affected by competitiveness. While it may be said that the average price can provide important information on the single route, it no doubt cannot satisfactorily illustrate how the price might change in the three months before the actual date of ? ght. In order to study the variables on which dynamic pricing depends, a regression analysis was carried out using parameter b as a dependent variable estimated on the single routes. The results are shown in Table 5. Length and route frequency are signi? cant variables with negative coef? cients. This means that the price trend will acquire steadiness as the route becomes longer, and more frequently travelled. In other words, Ryanair grants fewer discounts on long haul and high-frequency routes, despite advance purchase. A steady price trend may be partly justi? d when considering that Ryanair needs to cover fuel costs, and will try to do so on advance purchases as well. As regards the discounts offered, it seems that Fig. 8. Distribution of the number of routes according to coef? cients a estimated by analysing ? ight fares. Fig. 10. Comparison between the daily average price and the estimated price on CIA–STN route. 202 Table 4 Determinants of the average price. Variable Length Route frequency Ryanair ASK/departure ASK Ryanair ASK/destination ASK Overall taxation Departure GDP Destination GDP % Of fully booked ? ghts Departure population density Destination population density Total number of competitors Constant Adjusted R2 ? 0. 5668 P. Malighetti et al. / Journal of Air Transport Management 15 (2009) 195–203 Table 6 Determinants of the percentage of fully booked ? ights on single routes. Coef? cient (std error) 0. 021 0. 100 A9. 013 A8. 822 0. 298 A0. 71 A 10A03 A0. 46 A 10A03 24. 116 0. 43 A 10A03 0. 001 0. 038 1. 849 (0. 0010) (0. 0496) (3. 4414) (3. 2156) (0. 1119) (0. 0002) (0. 0002) (7. 4912) (0. 0008) (0. 0008) (0. 5403) (2. 6235) Statistic T 19. 98*** 2. 02*** A2. 62*** A2. 74*** 2. 7*** A2. 71*** A1. 74*** 3. 22*** 0. 52*** 1. 74*** 0. 07*** 0. 71*** Variable Length Route frequency Ryanair ASK/departure ASK Ryanair ASK/destination ASK Overall taxation Departure GDP Destination GDP Total number of competitors Constant Adjusted R2 ? 0. 1441 Coef? cient (std error) A0. 03 A 10A03 (7. 810 A 10A03) 0. 25 A 10A03 (0. 0003) 0. 062 (0. 0253) 0. 015 (0. 0238) 0. 92 A 10A03 (0. 829 A 10A03) 5. 07 A 10A06 (1. 72 A 10A06) 8. 30 A 10A06 (1. 71 A 10A06) 0. 006 (0. 0039) 0. 050 (0. 0192) Statistic T A3. 49*** 0. 68*** 2. 46*** 0. 65*** 1. 11*** 2. 94*** 4. 88*** 1. 55*** 2. 60*** nly minor discounts will be given on routes characterised by a high level of demand, because more frequent ? ights are provided. A negative coef? cient is also given for the percentage of fully booked ? ights, though its level of signi? cance is very low. The degree of importance of the departure airport is directly correlated to parameter b, which means that if Ryanair plays a dominant role in the departure airport, average prices are lower, and signi? cant discounts are more likely on tickets purchased in advance. The variable representing the number of competitors operating on the same route is positive, and bears a high level of signi? ance. This means that ? erce direct competitiveness on the same route does not lead to a decrease in average ticket prices, but rather induces Ryanair to grant greater discounts on advance bookings. The next section of the empirical analysis examines the determinants of one variable that has already been analysed in the previous regressions, namely the percentage of fully booked ? ights. The results of the relative regression analysis are shown in Table 6 (only explanatory variables which have registered a higher level of signi? cance have been listed).

Generally, short-haul routes from dominated airports present a higher percentage of fully booked ? ights. Also the GDPs of the areas linked with the airports contribute to an increase in the percentage of fully booked ? ights. All the analyses of variables were based on the optimum price function de? ned by Eq. (9), which has been drawn by considering an exponential demand curve with respect to price and advance purchasing time, as shown in Eq. (6). In the event that prices do not vary over time, the utility of potential customers tends to diminish, as tickets are booked well ahead of departure date.

The relative optimal price function is thus steady, and does not decrease as the date of ? ight approaches. This does not mean that special fares are not likely to be offered on speci? c routes. As a matter of fact, when the number of bookings does not meet expectations, the carrier is more likely to reduce prices in order to encourage people to book tickets, aiming to maintain Ryanair’s ? ight-? lling strategy. Yet, the effects correlated to demand variability do not seem, on average, to affect the price trend, consequently a downward course is unlikely.

The unlikelyhood of a downward course seems however to clash with some of the price trends observed on a number of Ryanair’s routes. Fig. 11 shows the average price for the Rome Ciampino– Shannon route, where it clearly reaches its lowest level between 50 and 60 days before the date of ? ight. A similar trend has also been recorded on other routes, although the downward trend observed as the date of ? ight approaches is not clear-cut and does not affect the average upward price trend that is typical of the last month before the scheduled departure.

In order to improve the statistical model, we used a demand curve equation with a different dependence with respect to advance booking, which led to the optimal price shown in Eq. (10). This kind of formulation presents a higher level of generality with respect to the previous analyses, and can be speci? cally obtained when coef? cients g and q equal zero. Hypothesising that prices are not subject to variation, from the previous assumption it may be inferred that the utility of potential customers does not present a steady increase as the date of ? ight approaches.

In other words, we admit to the possible existence of an optimal point in time when tickets are offered at a minimum price, as shown in Eq. (10). This new model was tested on all the routes analysed earlier in order to verify the actual improvement of price estimations. This has been con? rmed by the results, especially in the period between 60 and 90 days before the date of ? ight. In particular, the new estimates indicated that in 391 routes out of 550, the optimal purchasing period during which prices are at their lowest falls within 90 days from the scheduled departure date.

Fig. 12 shows the distribution of the optimal purchasing periods for the 391 routes. On average, the optimal purchasing period occurs between 50 and 70 days before the date of ? ight, as shown below. Table 5 Determinants of the dynamic pricing level (b coef? cient). Variable Length Route frequency Ryanair ASK/departure ASK Ryanair ASK/destination ASK Overall taxation Departure GDP Destination GDP % Of fully booked ? ights Departure population density Destination population density Total number of competitors Constant Adjusted R2 ? 0. 3756 Coef? cient (std error) A0. 22 A 10A03 (0. 16 A 10A03) A0. 15 A 10A03 (0. 0007) 0. 111 (0. 0524) 0. 042 (0. 0490) 3. 26 A 10A03 (0. 0017) 1. 65 A 10A06 (4. 040 A 10A06) 2. 95 A 10A06 (4. 088 A 10A06) A0. 078 (0. 1142) A0. 01 A 10A03 (0. 012 A 10A03) A0. 01 A 10A03 (0. 012 A 10A03) 0. 016 (0. 0082) 0. 326 (0. 0400) Statistic T A13. 50*** A2. 04*** 2. 13*** 0. 86*** 1. 91*** 0. 41*** 0. 72*** A0. 69*** A0. 81*** A0. 99*** 2. 03*** 8. 17*** Fig. 11. Comparison between the daily average price and the estimated price for the Rome Ciampino–Shannon route. P. Malighetti et al. / Journal of Air Transport Management 15 (2009) 195–203 203 ositively correlated to the dynamic pricing intensity. This means that direct competition on the same route does not lead to a decrease in average ticket prices, but rather induces Ryanair to grant greater discounts on advance bookings. While this paper represents a ? rst step in this direction, other factors should be analysed still in-depth, such as the temporal setting of the ? ight (namely time of day and day of the week). For instance, an improved measurement of the competitive pressure can be made through the analysis of the fares applied by Ryanair’s competitors. We leave it for future research.

Acknowledgements We wish to thank William Morrison and all the participants at the ATRS conference in Berkeley for their useful comments and ideas. We gratefully acknowledge the ? nancial contribution by ` MiUR (Ministero dell’Universita e della Ricerca) within program number 2005099094. References Alamdari, F. , Fagan, S. , 2005. Impact of the adherence to the original low-cost model on the pro? tability of low-cost airlines. Transport Reviews 25, 377–392. Alderighi, M. , Cento, A. , Nijkamp, P. , Rietveld, P. , 2004. The entry of low cost Airlines. Timberg Institute Discussion Paper, TI 2004-074/3.

Anjos, M. , Cheng, R. , Currie, C. , 2005. Optimal pricing policies for perishable products. European Journal of Operational Research 166, 246–254. Barbot, C. , 2005. How low cost carriers complete amongst themselves and with full cost carriers. 9th Air Transport Research Society Conference, Rio de Janeiro. Borenstein, S. , 1989. Hubs and high fares: dominance and market power in the U. S. airline industry. The RAND Journal of Economics 20, 344–365. Cassia, L. , Fattore, M. , Paleari, S. , 2006. Entrepreneurial Strategy. Emerging Business in Declining Sector. Edward Elgar, Cheltenham. Doganis, R. 2006. The Airline Business, second ed. Routledge, London. Franke, M. , 2004. Competition between network carriers and low-cost carriersretreat battle or breakthrough to a new level of ef? ciency? Journal of Air Transport Management 10, 15–21. Gallego, G. , Van Ryzin, G. , 1994. Optimal dynamic pricing of inventories with stochastic demand over ? nite horizons. Management Science 40, 999–1020. Gudmundsson, S. V. , 2004. Management emphasis and performance in the airline industry: an exploratory multilevel analysis. Transportation Research E 40, 443–446. McAfee, P. R. , te Velde, V. , 2006.

Dynamic pricing in the airline industry. In: Hendershott, T. J. (Ed. ), Handbook on Economics and Information Systems. Elsevier, Amsterdam. Pels, E. , Rietveld, P. , 2004. Airline pricing behaviour in the London–Paris market. Journal of Air Transport Management 10, 279–283. Piga, C. , Filippi, N. , 2002. Booking and ? ying with low cost airlines. International Journal of Tourism Research 4, 237–249. Pit? eld, D. E. , 2005. A time series analysis of the pricing behaviour of directly competitive ‘low-cost’ airlines. International Journal of Transport Economics 32, 15–38. Smith, D. , Bailey, J. Brynjolfsson, E. , 2000. Understanding digital markets: review and assessment. In: Kain, E. (Ed. ), Understanding the Digital Economy. MIT Press, Cambridge. Stokey, N. L. , 1979. Intertemporal price discrimination. The Quarterly Journal of Economics 93, 355–371. Wilson, C. A. , 1988. On the optimal pricing policy of a monopolist. Journal of Political Economy 96, 164–176. Zhao, W. , Zheng, Y. , 2000. Optimal dynamic pricing for perishable assets with non homogeneous demand. Management Science 46, 375–388. Fig. 12. Distribution of the optimal purchasing periods of time for 391 routes. 6.

Conclusions and future developments This work has provided an in-depth analysis of the pricing strategies of low-cost carriers. We focus on the features of the demand curve, hypothesising Ryanair’s ability to maximise its pro? ts. The price equation is obtained from an exponential demand function subject to Ryanair’s pro? t maximisation, and shows that, as the date of ? ight approaches, the price trend tends to resemble a hyperbola. The empirical analysis is based on an original database of Ryanair’s fares, made available on Ryanair’s website, for each individual route operated during the year starting the 1st July, 2005.

We estimate the price trends for each individual route over the 3 months prior departure, in terms of the average fares and the dynamic pricing intensity. In general dynamic pricing intensity is strong in almost all the ? ights. However the phenomena is complex in terms of determinants. We ? nd positive correlation between fares and route length, route frequency and the percentage of fully booked ? ights. Length and route frequency are also signi? cant variables with negative correlation to the dynamic pricing intensity. Ryanair grants fewer discounts on long haul and high-frequency routes, despite advance purchase. We ? d a negative correlation between the Ryanair’s importance in the departure and arrival airports and offered fares. The offer of the discounted fares appears as an incentive to use secondary airports. However, if Ryanair plays a dominant role in the departure airport, not only average prices are lower, but also signi? cant discounts are more likely on tickets purchased in advance. This indicates the importance for the carrier to ful? l its capacity. Surprisingly, the presence of competitors does not seem to heavily impact the average price. However, the variable representing the number of competitors operating on the same route is

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