Analysis Of The Cost Elasticity Variation With Passenger Demand For African Air Travel
Ssamula Bridget 	
 PhD student, University of Pretoria
and Researcher , Passenger Transport CSIR,
Pretoria, South Africa, 0001

ABSTRACT

The aviation industry in Africa is characterised by sparse passenger demand, such that even though there is increasing passenger growth as intra-African trade and movement is enhanced, there is still limited accessibility in between nodes, because the route demand is unpredictable. Even though regional expansion and entry of new competitors is a current trend for the African aviation industry, there is still a lot of uncertainty of the passenger demand needed to ensure that airlines will run profitably on given routes. In this paper, a cost model was used to calculate route operating costs for both direct routes and for similar routes on hub network, so as to develop a correlation between the cost elasticity variations with demand. This work would be an insight into understanding how the operating costs on a route vary when passenger demand changes, so as to enhance research to enable more airlines to make suitable choices in what route networks to serve, and how the changes in passenger demand will affect the operational costs. The main findings in this work show that a multiple linear regression is developed between GDP and air travel furthermore the trend of the exponential decrease in costs when passenger demand increases, is used to develop a linear logarithmic equation between the ratios of costs decrease and passenger increase on a hubbing.
Key Words: Demand Elasticity, Passenger Demand, African Air Travel, Hub Network Costs. 

INTRODUCTION
In 2004, International Air transport association (IATA) and African Airlines Association (AFRAA) estimated that the African air transport industry generated 470,000 jobs on the continent and contributed up to US$ 11.3 billion, representing 1.7% of Africa’s gross domestic product (GDP). Air transport development will enable African countries to: ensure rapid development and easier access to their territories at cheaper cost; consolidate their international and trade relations; boost foreign exchange earnings from airline operations, air service operators and suppliers and tourism; generate export earnings from agriculture (flowers, fruits and vegetables, fish and meat); and improve the control of famine and epidemics through rapid conveyance of foodstuffs and medicines, thereby making a concrete contribution to poverty reduction on the continent.. (UNECA, 2006) 
The growth in the African aviation industry has increased steadily the AFRAA 2000 annual report gives a summary of the air traffic movements.  Figure 1 shows the number and percentage of passengers carried in the various markets, between 1994 and 1999.  The report explains that the “Within Africa” market, which continued to grow, though was stunted between 1998 and 1999.  

Figure 1: African Air Travel Passenger Percentages

This was attributed to rationalization of operations, after the rush to introduce new services to and from South Africa after the democratic changes in the country in 1994, and also the withdrawal or reduction by a number of carriers of services during the year. The average number of passengers moving within the Africa region, as a percentage of passenger demand eas found to be 13%.
In 2004, the 42 member airlines of the African Airlines Association (AFRAA) transported 36 million passengers (12% increase compared to 2003) while European airlines (Air France, KLM, British Airways, Alitalia, Ibéria, Lufthansa, SN Brussels and Swiss) transported 72 million passengers from Africa, or 2/3 of the total African air traffic (108 million passengers). The recovery which started from 2003 is driven by airlines from North Africa (Egypt Air, Royal Air Maroc, Tunis Air, Air Algérie, Afriqihya), East Africa (Kenya Airways, Ethiopian Airlines) and Southern Africa (South African Airways). According to IATA, the growth rate of African air traffic in 2005 was higher than the world average: 11% compared to 8.3% for passengers; 8% compared to 3% for freight. This is corroborated by Boeing projections which predict a steady growth in African air transport of 4.8% for passengers and 6.4% for freight during the 2000-2019 period. Similarly, Airbus forecasts a passenger traffic growth of 6.3% for 2004-2013 and 3.9% for 2014-2023, and a freight traffic growth of 7% for 2005-2023 (UNECA, 2006)
PROBLEM STATEMENT
There are many problems facing the African airline industry some of which include: high airfares, sparse passenger traffic, and inaccessibility within different parts of the continent. Even though regional expansion, liberalisation, privatisation and entry of new competitors is a current trend for the African aviation industry, there is still a lot of uncertainty of the passenger demand needed to ensure that airlines will run profitably on given routes. The aviation industry in Africa is characterised by sparse passenger demand, such that even though there is increasing passenger growth as intra-African trade and movement is enhanced, there is still limited accessibility in between nodes, because the route demand is unpredictable, for the sustainability of air travel between nodes. 

Inelastic Demand
The elasticity of demand is the percentage change in demand compared to the percentage change in price. If the elasticity is below one, it means that the market is inelastic. In other words, the demand is not very sensitive to the price. If elasticity is greater than one, then the market is elastic, that is, a percentage rise in price would result in a greater percentage reduction in demand. (Chingosho, 2005) 
Source :( Chingosho, 2005)
Figure 2: Elasticity of Demand for All Travellers
The elasticity of demand for all air travellers both business and tourism, worldwide is shown in Figure 2, and  is found lowest in Africa and highest in the USA. This is a reflection of the limited options available to travellers within Africa (Chingosho, 2005). 
High Aircraft Utilisation
Figure 3 shows the average number of destinations, aircrafts flies to within a specific region, showing that African fleet are utilised twice as much as aircraft in other parts of the world. Most of the smaller African airlines with fleet sizes of three to ten aircraft, which fly one to three times a week to some destinations. 
This compares unfavourably with the practice by the larger carriers from Europe and the Middle East that have daily or multiple daily flights to some of their destinations. This is very convenient for travellers, particularly business people. This puts African carriers at a competitive disadvantage. This implies that African airlines need to restructure their operations to ensure frequent services (minimum four times a week) to their domestic or regional destinations. Instead of flying to too many destinations with a small fleet, it may be necessary to concentrate on a limited number of destinations to achieve high frequency of services.

Figure 3: Average number of destinations per Aircraft
Low Load Factors
Load factor is the ratio of the revenue passenger kilometres (RPK) to the available seat kilometres (ASK). Over 50 percent of most African airline costs are fixed. Because of the low marginal costs of carrying additional traffic, load factors are a critical determinant of profitability. 
Figure 4: Worldwide Load Factors
Figure 4 shows that the Africa region has the lowest load factor at 62.56 percent compared with other regions of the world. The Far East and Pacific regions have relatively high load factors, averaging 76.32 percent. Asia and the Middle East have load factors closer to those achieved in Africa. The low load factors are a reflection of the thin routes on the African region. The routes are thin because of the much higher air fares compared to other regions of the world and a relatively poor population.
There is increasing pressure for government airlines in Africa to improve efficiency whilst making a profit margin in the face of issues like: privatisation, alliances with foreign airlines and more stringent aviation standards of security and noise.  This implies that for liberalisation within African skies, as suggested by the Yamoussoukro Decision, an analysis needs to be done on the economics of an African regional airline.  Some traditional airlines like South African Airways, Ethiopian Airlines and Kenya Airways, are actively pursuing expansion within the continent by providing direct flights for lucrative routes whilst hubbing at their home airports of Johannesburg, Addis Ababa and Nairobi respectively to consolidate passenger demand.
The aim of this paper will be to understand how the operating costs on a route vary when passenger demand is consolidated in hub and spoke networks in Africa, so as to enhance research to enable more airlines to make suitable choices in what route networks to serve, and how the changes in passenger demand will affect the operational costs.
DEMAND ELASTICITY
The three fundamental factors affecting passenger demand are incomes, fares and service levels.  Broad estimates of aggregate elasticity’s imply that demand is highly elastic with respects to fares and relatively inelastic with respect to service levels.  The components of air travel demand are co-related in Figure 5.

Economic Growth (GNP)

Population

Actual market
=
Passenger-Kilometres

Effect of fares
Elasticity -0.5 to -1

Number of flights and routes
Elasticity 0.1 to 0.5

   				   Elasticity 1 to 2

Figure 5: Factors affecting demand for air travel
In this study, demand elasticity is going to be compared with two elements which are fares and income, and service level will not be measured, due to lack of availability of data.
DEMAND ELASTICITY WITH INCOME 
An elastic relationship between the GDP per capita each county and the number air travel passengers, is suggested showing that the high-income elasticity can be seen in the short-term series relationship between economic activity and air travel demand.  
Taneja (1978), suggest that since GDP is a measure of the economic well-being of people within a nation, It can be assumed that, the higher the GDP, the greater the output of goods and services, the better off people are, and the more they will travel for business, personal and pleasure reasons.
Although air travel tends to grow faster than GDP, it still follows very closely the cyclical pattern in GDP.  (Hanlon, 1999). An analysis of international air transport trends shows a close relationship between international demand for air transport services and income trends. Passenger traffic growth variations are wider than income growth variations. However, some long-term studies of the air transport sector have shown that such sensitivity to world economic variations seems to be reducing steadily. Hence, according to a study conducted by the firm, Arthur D. Little, (and challenged by some experts) “the elasticity of international air transport to GDP has been declining steadily since 1970 and is approaching 1”. Table 1 show that the gap between air transport sector growth and GDP growth has been narrowing over the last three decades: 
Table 1: Comparison of air traffic and GDP growth rates over the last three decades 
 	1971-1980	1981-1990	1991-2000	
Air traffic growth rates	6.7 %	4.4 %	3.3 %	
Economic growth rate	3.7 %	3.0 %	2.6 %	
				
(Source: Chingosho, 2005)
According to the authors of the study, such convergence reflects “a greater maturity of the markets and the growing influence of the price factor”. It has been proven that during stable periods, the average growth rate of air traffic is double that of GDP (with an average annual growth of 6.5% in world traffic for an average GDP growth rate of 3.1%, over three decades). (Chingosho, 2005)
Methodology
To apply the relationship between GDP/capita is needed. But to relate this to the number of passengers, the rate would need to be multiplied by the population i.e. trips/person = f (GDP/capita) 
World Bank data query is an online database that is used to find out data from different countries, spanning from 1997-2000 for various economic indicators. For this study, the database provides information for all African countries on population, GDP (US$) and aircraft departures/year. 
Multiple Regression analysis is to be run on the aircraft departures, GDP or GDP per capita from each panel data, to create a multiple linear regression equation, using the least squares technique.  

On analyzing the data the independent variables (i.e. GDP, Population, and GDP per capita) simultaneously affect the dependent variable (i.e. aircraft departures), judging from the values of the R2and multiple regression equation is shown Figure 6;
Figure 6: Graph showing GDP trend line with aircraft departures
Linear regression analysis gives a correlation of 0.833, with an R2 of 0.694 but it does not put into consideration exogenous factors like unemployment, route fare, tourism attractions, etc which in essence do affect the number of air travel passengers. That is why when the cubed power is used instead; it implies that there is more than one factor, which is responsible for the movement of people, from one country to another. Therefore, a trend line with increasing factors all elements in the GDP gave better R2 values of 0.7885.  
DEMAND ELASTICITY WITH OPERATING COSTS
Marketing expenditure serves two functions: one is to increase the airline's share of passenger demand; the other is to make that demand less price elastic.  Figure 7 shows that the original demand curve before anything is spent on marketing is represented by D1.  On this schedule, if the fare charged by the airline is P1, the number of passengers carried by the airline is Q1.  Following a marketing campaign, the demand curve shifts to the right and acquires a steeper slope.  

The rightward shift allows an increased number of passengers Q2 to be attracted to the service at original price, and the steeper slope enables the airline to raise the fare and still have a substantial increase in passengers.  From Figure 7, the fare can be raised to P2, at which passenger demand is Q3, still well above the original level of Q1.

B

D1

C

D

D2

     Fares       P2

       P1
									
Q1	Q2		Q3
				Demand
Figure 7: Original Demand Curve for Passenger Demand (Hanlon, 1999)
The airline benefits both from an increase in passengers and from a higher fare per passenger; its total gain in revenue is the shaded area Q1ABQ3 from the increase in passengers plus area P1BCP2 from the increase in fare.  So long as this additional revenue is greater than the costs associated with the marketing campaign, the airline increases its profit. (Hanlon, 1999) 
Economies from route traffic density arise because greater density enables the airline to use larger aircraft.  These are more efficient with lower costs per seat mile and/ or to operate at higher service frequencies and consequently at higher seat load factors, which lead to lower cost per passenger mile (Doganis, 2001).
O’Kelly et al., (1987) in analysing the effect of increase in discounts on hub links as passenger flows vary, found that for H&S network, costs increase at a decreasing rate as passenger flows increase. As shown in Figure 8, with the non-linear function effect in their model, agglomeration of flows provides a benefit in that, the rate at which the per mile travel costs increase, decreases as flows increase, unlike the conventional HUBLOC model which implies that as the flows on hub links increase the discount stays constant.

Source: O’Kelly et al. (1987)
Figure 8: Costs per passenger-mile: non-linear cost function and HUBLOC model
From this literature, a study to understand how increase in demand affects the in operating costs is vital to develop a relationship between the rate at which increase in demand affects the costs of travel.
Methodology
The methodology followed will verify whether demand is elastic with fares especially as fares decrease and passenger numbers increase. Passengers are going to be consolidated through designing hub and spoke networks, where passengers from their origin are consolidated to hubs before reaching their final destination to benefit from some of the advantages of hubbing with respect to Africa’s situation as shown in Table 2. A cost model whose schematic is shown in Figure 9 is used to calculate routes operating costs used in a hub network, using their existing  and consolidates O-D demand is used to derive the operating costs. The main output of the cost model is to calculating route operating costs for any given route in Africa, for 11 different aircraft types commonly used among major African airlines, such that the choice for the most efficient aircraft to fly a route using present route characteristics of passenger demand and sector distances (Ssamula, 2004).

Table 2: Hubbing benefits that would benefit the African aviation industry
Merits of Hubbing	
Economies of Scale	The most obvious difference between the two networks is that the passengers who fly using the hub network for the route are greatly increased. This is because all the people on the first leg of the route include all passengers to and from the origin and the last leg of the journey includes all the passengers who fly to and from destination. The economies of scale that are realised through consolidating passengers are seen in the lowered costs of supplying the service and the cost per passenger that greatly decrease through hubbing.	
Higher flight frequencies
	The major difference for short haul routes between the direct and hubbing is that for the direct route, only the passengers flying the O-D pair will use that route, while in hubbing, all flow from the origin node, must go through the closest hub. This implies that the passenger numbers from the origin leg in hubbing are much higher, and the flight frequencies needed to meet the increased passengers would result in higher flight frequencies	
Better Capacity Allocation	Due to the short flight time, the fleet size remains fairly low whether the passenger demand increases, since one aircraft can fly the route as often as the minimum daily frequencies can be met. The implication of the increased frequency of flights brings up important factors like congestion and available slots especially at the hub airport, needed to meet the increased passenger demand	
High average yield	The lower operating costs achieved with consolidating passengers means that airlines have the flexibility of choosing a fare that ensures that they can run profitably for most of the routes. Node and hub airports also have increased sources of income derived from increased passenger handling fees and landing fees, with increased passenger demand and higher flight frequencies.	
Job creation	Due to the increased capacity of airports, higher passenger numbers the economic generating capacity of airport increases, thus creating more employment both in and around the airports especially the hub airports	
Lower cost of Travel	The costs per passenger exponential decrease with increasing passenger, is achieved with hubbing. This implies that airlines can afford to fly fuller planes at low costs especially if the load factors can be achieved, and in turn the cost of travel on the routes are decreased, no only to attract more passengers to fly, but also because the operating costs are low.	
Increased Accessibility	Due to increased flight frequencies which are necessary to meet the higher passenger demand from origin and destination nodes and along the hub-hub links, passengers are allowed flexibility of being able to fly more frequently at a low cost from one node to another.	

 Figure 9 shows the flow chart layout of the calculations to be done and what information is required as input to give the output data service analysis needed.

CALCULATION

OUTPUT DATA

Standing costs
•	Depreciation
•	Insurance
•	Interest

Flying costs
•	Fuel and oil
•	Labor
•	Maintenance

Other costs
•	Landing fees
•	Passenger fees
•	Marketing
•	Administration

Total costs
•	Return flight per aircraft
•	Weekly flight per aircraft
•	Weekly cost for fleet
•	Annual cost for fleet

Costs per
•	Per passenger
•	Per available seat-km
•	Per aircraft-km
•	Per passenger-km

Graphic outputs
•	Cost structure for mode
•	Per mode per aircraft-km
•	Per mode per varying distance
•	Per mode per varying passenger demand

Passenger data

Route distance

Block time

Annual utilization

Fleet size

Weekly aircraft trips

For each aircraft type

Round trip time

INPUT DATA

Maximum daily and weekly flights 

Minimum flights per week

AIRCRAFT SPECIFICATIONS

ROUTE CHARACTERISTICS

Figure 9: Model flow chart

Application to hubbing
The model developed was able to calculate the cost parameters incurred while supplying a transport service allowing the user can then make an informed choice on: least costly aircraft type, lowest operating costs, highly utilised fleet size, economically efficient service, varying passenger demand. The cost structure, equations and default values were collected from various literature sources and focus was put on the operating items which where divided into the standing, flying and other costs. One of the applications of the cost model is that it can be tested for the economies achieved in higher traffic densities. This was done by calculating the costs per passenger as the passenger demand increases on the same route for the 11 different aircraft. As shown in Figure 10, the cost model results portray the general trend of the costs for transporting flow decreasing exponentially as passenger demand increases.  The application to hubbing can be seen when cost of flow reduces exponentially as passenger demand increases which shows the viability of designing of a hub and spoke network which works through consolidating passenger traffic on shorter routes within Africa. (Ssamula, 2006)

Source (Ssamula, 2006)
Figure 10: Exponential decrease of costs with increasing passengers

Hub network design
In this paper a hub is defined as a hub defined by route structure, where it serves as a distribution point for air travel to and from it surrounding area, with connecting services, irrespective of the number of originating passengers. The procedure followed in designing a hub network, involves first locating the hub airports, using cost effective methodologies through which all the flow will pass. After locating the hubs, the nodes are then allocated to the hubs using single assignment to the closest hub, before reaching their final destination. After the pattern of flow for the network has been established, the passenger numbers along each link calculated, such that all passengers are routed from their origin to their destination at least one hub and a maximum of two hubs. (Ssamula, undated)
Assumptions 
1.	The aircraft departures are multiplied by a factor of 15% (AFRAA, 1999) to calculate the aircraft departures moving only within Africa. Passenger numbers are calculated from the product of aircraft departures and an assumed average aircraft seat capacity assumed to be 200, at a at a 0.626 load factor derived from Figure 4.
2.	Since comprehensive Africa O-D air travel data is hard to find, the O-D trips are developed using the Furness’ method for a doubly constrained matrix. In O-D matrix is developed using a gravity model, which assumes that the probability of a trip between two nodes is assumed to be proportional to the distance between each O-D pair assuming a β be 0.14, with an average aircraft speed of 800km/hr and  was calculated to be 52.02.
3.	Africa faces the dilemma of not having many international airports with capacity, demand, market size and infrastructure for hubbing due to the low levels of income for most countries and the expense associated with air travel and its infrastructure. Therefore possible hub airports will be chosen based on the operational effectiveness in terms of location within the network.

4.	Competition on each of the routes in the network is neglected, because of the lack of availability of data about the competition levels and market share on routes; furthermore because of the low passenger demand, many of the routes within the continent have only one airline option within the African network, so assuming a level of competition would not be practical for all the routes in the network.
5.	One of the benefits of hub and spoke networks, is the in choosing hub options with short haul distances to nodes. The economic benefit of flying shorter routes is such that one can use smaller cheaper aircraft, even when flight frequencies are high.  Hubs are therefore chosen  such that the distance from the node to its closest hub is not more than 3,500km
6.	The costs per passenger calculated by the cost model are not representative of the fares for the route, but should be taken as the marginal costs per unit flow derived from dividing the operating costs for the route derived from the cost model output by the demand on the route
Data compilation and analysis
A total of 14 hub and spoke networks were designed, and the passenger numbers and operating cost per passenger for each of the Hub-Hub links in each network are compiled and compared with their original O-D passenger numbers and costs in the trip generation matrix. The ratio of the costs decrease and the passenger increase for each node was calculated. Figure 11 shows that the ratio of costs decrease; decreases exponentially with the ratio of passenger increases. 
Figure 11: Exponential decrease with which ratios of costs decrease as passengers increase with hubbing
The exponential element implies that when the passengers increase greatly by ratios, the operating costs decrease ratio will reduce due to the fact that the costs of transporting the passengers is equally as high due to higher flight frequencies, higher capacity aircraft  and larger fleet size needed to meet  exorbitant demand.
To derive the exponential relationship between the ratios of costs decrease and passenger increase, the logarithmic function of the ratios are calculated and Figure 12 shows the linear relationship for the function which relates the rates at which costs will decrease as passengers decrease.
Figure 12: logarithmic relationship between passenger increase ratio and costs decrease ratio 
The scatter plot for the logarithmic ratios shows a linear regression with an R2 of 0.9008 and a correlation of 0.845. The equation shows that a relationship can be developed using the ratio with which passengers increase and that this equation can then be applied to passenger increase rates and that can be extrapolated in terms of increased operating costs for various routes. 
CONCLUSIONS 
The aim of his paper was to use a desktop study using exiting passenger demand values to verify whether passenger demand in Africa can be predicted using the existing data sources. Africa’s problems in the aviation industry with specific reference to the unpredictability on passenger demand elasticity with costs, is a major problem for sustainability of airlines even with the institutional backing of regional liberalisation through the Yamoussoukro Decision.
Literature which shows elasticity of demand with income is verified using available World Bank sources to suggest a probable relationship which has many factors that affect increasing air travel aside GDP like security, tourism, which are difficult to measure and quantify. The findings in the study prove that there is a correlation of 0.833 and a multiple linear regression between GDP and air travel, due to the fact that there are many unquantifiable indicators.
Further more, literature studies show the relationship which implies that operating costs are lowered when passenger demand increases.  Passenger demand elasticity is then test for the elastic relationship it is known to have with costs, especially when the passenger demand increases. The methodology entails: developing an O-D matrix using a gravity model based on aircraft departures, then calculating the costs per passenger for routes using a cost model developed to calculate route operating costs. Hub and spoke networks are then designed through which demand is consolidated such that all flow from the origin is routed via at least one hub before it reaches its final destination. The costs per unit flow calculated using an operating cost model and the rates at which the passengers increase is compared to the rate at which the costs decrease, these ratios have an show the conventional exponential decrease between the rate at which costs decrease when passenger numbers increase, which flattens out  as passengers increase. Thereafter the logarithmic ratio of passenger increase and the logarithmic ratio of cost per passenger when passengers are consolidated on a route are analysed to show a correlation of 0.845 and good linear regression of 0.9008. 
This study shows good potential of African air demand patterns which are shown to follow literature study finding and the general trends, which is a good starting step to be able to understand the market that uses air travel in Africa. The ability to forecast demand still remains a challenge in the face of incomplete or non existent datasets, due to unpredictability of the market and the high ability of the aviation market to be influenced by exogenous factors like security, economic growth, trade, tourism potential etc, which are difficult to quantify.

References
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O’Kelly, M.E. (1987) ‘A quadratic integer program for the location of interacting hub facilities’, European Journal of Operational Research 32, pp 393-404
Ssamula, B. (2004) Developing a cost model for running an airline service, Masters Dissertation, University of Pretoria, South Africa.
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Ssamula, B.  Cost Effective Strategies to design a hub network for sparse travel demand within Africa, PhD thesis, University of Pretoria (under review)
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