M Pigeon

C Morlaas

H Aubert

B Souny

Highly Compact Composite Antenna

Introduction

These last four decades have seen a race to miniaturize the Radio-Frequency part of popular devices. The antenna has to present not only very high compactness but also a very good integration with the surrounding devices. Decreasing the antenna size concentrates the electromagnetic fields in the radiating structure formed by the antenna. So the associated quality factor increases a lot and the bandwidth decreases. Moreover the antenna losses increase and so the efficiency decreases. A trade-off has to be found between the size, the bandwidth and the efficiency of the antenna (see, e.g., [2]). An original solution combining high compactness and excellent integration capabilities is proposed in this communication. It consists of the particular combination of two equivalent magnetic and electric current distributions. Contrarily to the classical small ceramic microstrip antenna [START_REF] Yeh-Chian | Small-size surface-mountable circularly polarized ceramic-chip Antenna for GPS Application[END_REF], this composite solution can be advantageously used at low frequency regimes.

The magnetic/electric dipoles composite antenna

The proposed antenna is shown in Fig. 1. The flattened helical part is equivalent to an inductance placed above a metallic plane (1,5mm above). Capacitances are distributed between the helical part and the metallic plane. Such radiating element is equivalent to an electric loop loaded with a capacitance. It consists of a shorted half-wavelength helical line and its modes are those of the half wavelength antenna. The helical part can be replaced by equivalent magnetic current source M as shown in Fig. 1. The version of the helical part to one loop only is equivalent to the Wheeler loop [3]. However the distributed capacitance between the helical part and the metallic plane facilitates in the present antenna the fabrication by using the classical printed circuit technology. In the region where the electric field takes high values (i.e., in the shores of the helical part) the excitation of the helical part is achieved by electrical coupling. The excitation consists of a microstrip line (see Fig. 2). The length, the width and the proximity of this excitation line from the helical part achieve 50Ω impedance matching. The excitation can also be performed by using the magnetic coupling via the loop located at the center of the helix but we have observed that a good coupling is difficult to reach in practice. The second part of the antenna is the metallic plane placed below the helical part. This metallic plane supports equivalent electric current density distribution generated by the abovementioned magnetic current distribution (see. Fig. 3). Consequently the electromagnetic field radiated by the antenna consists of the combination of the fields radiated by the above-mentioned equivalent electric and magnetic current distributions. The antenna radiates a linear polarized field. Constructive interferences can be achieved above the metallic plane while destructive interferences can be generated below this plane. The dimensions and the distance to the helical part of the metallic plane control the radiation pattern and the efficiency of the composite antenna. Since the electromagnetic field is highly concentrated around the helical part of the antenna, the performances of the proposed radiating element are not sensitive to the surrounding (e.g., components or circuitry located on the metallic plane).

Design and realization of the composite antenna

The chosen operating frequency is 1.575GHz. The center part length, width and height are denoted by respectively L, W and H. The number of loops, the width of the printed microstrip lines and the distance between the lines are denoted respectively by N, a and d. From the dispersion diagram of the helical line corresponding to given W, H, a and d of an elementary cell we can derive L. The phase velocity V' of the elementary cell and the phase velocity V of the same size cell in free-space are derived from this diagram. Next, from the equation V/V' = λ/λ' where λ denotes the free-space wavelength, we determine the wavelength λ' from which the length L is derived (L=λ'/2). Finally we deduce the antenna characteristic parameter: L=15mm, W=15mm, H=3,05mm, N=2, a=2,5mm and d=3,5mm. This theoretical length L has to be reduced in order to compensate the edge effects. The finite-sized metallic plane (50x50x1.57mm 3 ) is obtained from the metallization of a glass-Teflon substrate (ε r =2.55). The resulting antenna is shown in Fig. 1.

Electromagnetic simulation and measurement of the radiation characteristics of the composite antenna

The HFSS electromagnetic simulations (including losses) allow us to predict the bandwidth and the efficiency of the antenna around its operating frequency. The simulated bandwidth is 6.5MHz. As shown in Fig. 4, measured results are in good agreement (bandwidth = 8MHz) compared to simulated one. Moreover the directivity pattern of the composite antenna is analogous to one of the (simulated) microstrip antenna (18x18x4mm upside a 50x50mm metallic plane) operating at the same frequency for a θ cut in a z0y plane (see coordinate system Fig. 2) as shown in Fig. 5. Note that the maximum directivity is about 4.2 dBi. The simulated efficiency (87%) of the microstrip antenna is found to be higher than one of the composite antenna (50%). In Fig. 6, we compare in the z0y plane the normalized radiation patterns. Note that the results of simulation and measure match correctly. However, contrarily to the classical small ceramic microstrip antenna [START_REF] Yeh-Chian | Small-size surface-mountable circularly polarized ceramic-chip Antenna for GPS Application[END_REF], this composite solution can be advantageously used at low frequency regimes.

Conclusion

The highly compact antenna proposed in this communication consists of a judicious association of equivalent magnetic current source with equivalent electric current source. This composite antenna presents a directivity radiation pattern analogous to one of the microstrip ceramic antennas but can be used at low frequencies. The antenna measurements confirm the promising performances obtained from electromagnetic simulations.

[ 2 ]

 2 J.S. McLean, « A Re-examination of the Fundamental Limits on the Radiation Q of Electrically Small Antennas », IEEE Transactions on Antennas and Propagation, Vol.44, NO. 5, May 1996. [3] H.A. Wheeler, « Small Antennas », IEEE Transactions on Antennas and Propagation, Vol.AP-23, NO.4, July 1975.

Figure 1 :

 1 Figure 1: The composite antenna

Figure 3 :Figure 4 :

 34 Figure 3: Equivalent electric current distribution

Figure 6 :

 6 Figure 6: Radiation pattern (dBi) of the composite antenna (a) simulated, (b) measured.


Estelle Malavolti
email: estelle.malavolti@enac.fr

Julien Jenvrin

Strategic reaction of airlines to the ETS *

The air transport sector is about to enter the European Trading Scheme progressively in 2011. The regulation of the CO2 emissions means for airlines more costs and a modification of the organization of their market. Our paper proposes a precise model of nonetheless the regulation but also of airlines CO2 emissions. Our conclusions are twofold. Firstly, although profits are negatively impacted by the introduction of the ETS, a monopoly airline carries more passengers at a lower price. Two opposite effects are at play: the marginal cost increases as polluting becomes costly, which results in an increase of the price. However, there is a second effect that makes the price decreasing: the way the free allowances are given creates a bias towards more activity. We show that more activity is reached at the equilibrium. De facto, more CO2 is emitted. Nevertheless, we show as well that it is profitable for the airline to buy a new aircraft because the marginal cost decreased. Again more activity is reached at equilibrium but at the cost of less CO2 emissions.

Introduction

The air transport sector in Europe will be fully included in the European Trading Scheme (ETS) in 2012. Despite the relatively low level of greenhouse gas emissions (only 3% of the total European emissions), this sector has known a rapid growth until recently: From 1990 to 2005, the EU aviation emissions increased by 87% and it is expected to double from now to 2020 (See Commission Staff working document 2006 and EU directive 2003/87/EC). On top of this, the air transport sector is also responsible for other releases like nitrogen oxides, water vapor or noise, which effects are not easy to account. Nevertheless, a regulation of these external effects is to be expected. It is thus important to evaluate which impacts a regulation may have on the market and its organization. Our paper offers a precise model of nonetheless the regulation but also of the emissions of the airlines. The regulation system includes two different elements: the first element concerns free allowances that will be given to airlines according to their current activity. The second element is the payment of rights to pollute on the CO2 market. There is a strategic stake in the setting of the "free of charge" quotas, since their number depends on the activity of the airlines: with the system, the airlines will receive a number of rights to pollute proportional to their activity. On the other hand, the rights to pollute, i.e. the internalization of the pollution, will represent an additional cost, which will be higher, the higher the activity. As a consequence we have paid very much attention to the modelization both of the regulation and of the production of emissions. We model the emissions as a joint product of the airlines activity that comes from the utilization of the fuel. Hence a particular attention is given to the estimation of the fuel cost function, which is calibrated with the use of real data. In the economic literature, pollution is modelled as an externality which is not taken into account by the market (see for instance [START_REF] Laffont | Fundamentals of Public Economics[END_REF]. The focus has then been made on the way to "internalize" pollution. Several instruments have been put forward (taxation, subsidies, allowances trading ...) resulting in State intervention, and the literature deeply analyses the efficiency of these different tools (See for instance B. [START_REF] Salani | The Economics of Taxation[END_REF] or G. [START_REF] Myles | Public Economics[END_REF]. Our work builds on this general literature focusing on the specificities of the air transport sector to model the impact of an environmental regulation. The environment problems have raised several questions. For instance, Portney (2005) makes a review of the existing regulations and tries to evaluate what will be the regulations of the future. Among the economic tools used to regulate, the taxation is the means which has the most received attention. [START_REF] Barthold | Issues in the Desing of environmental Excise Taxes[END_REF] presents the different taxes used for environmental regulation and their efficiency to regulate emissions. We chose to model the ETS as an increase of the variable cost, which means that it can be apparented to a tax (or a subsidy) on the airline activity, because the regulation is designed as such. A particular attention will be given to the study of the use of the fuel by airlines because of its direct relationship with CO2 emissions (See the IPCC report 1999 for an evaluation of the impact of aviation on global atmosphere and the EU Directive 2007/589/EC for the determination of a precise coefficient linking fuel consumption and CO2 emissions). [START_REF] Harris | An Economic Model of U.S. Airline Operating Expenses[END_REF] made an exhaustive analysis of the US airlines operational costs. [START_REF] Miyoshi | The carbon emissions of selected airlines and aircraft types in three geographic markets[END_REF] focus on the evaluation of the carbon emissions of airlines. They propose an original methodology to compute these emissions. We use our own method to evaluate the emission, presented in appendix, but the focus of our paper is more on the economic modelling of the ETS consequences on airlines and their strategies. Besides, we chose to model the externality as a joint production of the airline activity. Models of joint production are presented for instance by [START_REF] Baumgartner | Joint Production, Externalities and the Regulation of Production Networks[END_REF][START_REF] Baumgartner | Joint production[END_REF]. Our paper is also directly related to papers such as the one by Viera et al. In section 2, we present the European Trading Scheme and how it will be implemented to the air transport sector. A modelisation of this system is then introduced and stylised facts on some financial consequences for airlines are shown. This section ends with the economic model we propose to involve all these elements. In section 3, we derive the results and give interpretations, which proofs are placed in appendix. Section 4 concludes.

Modelling the impact of ETS on airlines 2.1 Legislation design and benchmark R

In order to define a model as close to reality as possible, we have to go into the tecnical details of the legislation. This will help us to define the relevant parameters and anticipate if possible, the major impacts of the legiclation on airlines. Airlines will receive at the beginning of each period allowances to emit CO2 and they must surrender at the end of the period the number of allowances equivalent to their total CO2 emissions. To determine the number of allowances given to each airline, the EU will rely on the average level of emissions during the years 2004-2006. The total number of allowances is a sum of three elements:

N T = N a + N r + N f ,
with N T the total quantity of allowances for a period, N a the number of allowances to be auctioned for the period, N r the number of allowances in the special reserve and N f the number of allowances to be allocated free of charge for the period.. It is worth noting that N f = 82% × N T : Only 82% of the total allowances will be allocated free of charge to the airlines.

Creation of a benchmark

To allocate allowances free of charge to aircraft operators, the EU uses a benchmark. This benchmark is expressed as allowances per tonne-kilometer carried and is calculated by dividing the number of allowances to be allocated free of charge in a period by the sum of the tonne-kilometer data included in applications submitted to the Commission. The use of a measure of the mass multiplied by distance type allows to harmonize the difference of network between airlines. Let us define W i as the total tonne.kilometers carried by airline i. Then, R = N f i Wi . The number of allowances allocated to the airline i is obtained by multiplying R with the total tonne.kilometers carried by the airlines W i . The problem is to give a value to R. We consider the airline i, for all its route j covered 1 we define D j (distance of the route covered by an aircraft, expressed in km) and Q j (sum of tonnes carried by the airline on the route on the period). Thus, for this route Y j the tonne.kilometers carried are:

Y j = Q j D j .
The total tonne.kilometers carried of the airline i is W i = j Y j . Let us now introduce c j , the average consumption of fuel, expressed in liter per tonne-kilometers of an aircraft on a given route j. For each route, the average consumption of fuel is equivalent to the fuel consumption divided by the total tonne.kilometer carried. So for each route j, we have information about the couple (c j , Y j ) and we can compute the total fuel consumption of the airline i as C Ti = j c j Y j . Then we define the average consumption per tonne.kilometer of the airline i as c meani = C T i Wi = j cj Yj j Yj . With C T otal the total Jet fuel consumption of all the couple (route, aircraft) and all the airlines concerned by the ETS, we can apply the same method and define c EU as the average consumption expressed as liter per tonne-kilometer of all the aircrafts and all the routes concerned by the ETS system c EU = C T otal i Wi . Now let's we introduce the constant λ expressed in T CO2 /L which corresponds to the tonnes of C02 emitted by burning one liter of fuel (λ = 2.52 -3 Tonnes/L)

R = N f i W i = 82%N T i W i = 82%λC T i W i = 82%λc EU × i W i i W i = λ82%c EU
To understand the consequences, especially financial ones, for the airline i, we have to compute the difference between the real quantity of CO2 emitted expressed in tonnes (λc meani W i ) and the allowances allocated by the EU to the airline (RW i ):

λc meani W i -RW i = (λc meani -R)W i = λ(c meani -82%c EU )W i 2.1.

The EU choice and the consequences for the airlines

Notice that variable c meani is a measure of the fuel efficiency of the airline i. Indeed, the lower the average consumption per tonne.kilometer carried the more efficient the airline.

The EU ETS system could have been based only on CO2 emission of each airline and then could have given to the airline a certain percentage of their monitored emissions. But such a system would have rewarded the highest polluter, but not the most efficient one. This would not have been a good incentive for the airlines to be fuel efficient. So the EU system with the benchmark R, based on the tonne.kilometer carried, will reward the efficient airline (i.e.

the one with the highest W i and the best c meani ). Technically, the EU system relies on the gap between the average consumption of the sector c EU and the average consumption of the particular airline considered c meani . Indeed, if c meani > 82%c EU , airline i has to acquire allowances. The level of reference 82%c EU thus stands for the standard efficiency level of consumption. The EU compells the airlines to monitor and report, for each route concerned by the ETS, both their tonne.kilometers carried and the CO2 emissions. Indeed, the idea

1 j is a finite number.
is that the total CO2 emissions will be used to design the benchmark R of the next period.

The tonne.kilometers carried will be use both to design R and to set the free of charge allocation. What can we guess about the different strategies of airlines with respect to this monitoring/reporting? Like we noted above, according to the ETS, airlines best strategy is to decrease at maximum their consumption c meani . Nevertheless, if airline i is big enough, this will also reduce c EU , which is less interesting. Hence big carriers might have less interest in improving their average consumption. However, the maximum gains from a decrease of the average consumption are reached for a no reactions from other airlines (ceteris paribus condition). Suppose every airline is decreasing c meani , then the average consumption of the whole sector is decreased and the total impact is not clear cut, i.e., whether improving its system decrease the number of allowances required). Logically, we have the same not clear cut impact about the reported emissions. By reporting "inflated" emissions an airline makes the benchmark R raised (which is a good point) but it has to surrender a higher number of allowances (so, has to buy more allowances on CO2 markets). Concerning the monitored tonne.kilometers, we have a kind of prisoner's dilemma. Indeed, each arline has an interest in "inflating" their tonne.kilometers carried to receive more free allowances. But if all the airlines do that, the benchmark value decreases. So the total impact is ambivalent. However, when an airline is a small one and so has not a great impact on the benchmark value, it is always interesting for it to "inflate" its tonne.kilometer carried and consequently to receive added free allowances.

Stylised facts: financial impact of the ETS on some airlines

The idea of this paper is to evaluate the future impact of the ETS on the airline cost, through the use of an economic model. Several parameters will be at play and induce different impact according to airlines: the fleet (type and age), the network, the type of activity (short-haul, long-haul), the load factor, the flight optimized procedures and the airline strategy. We try to evaluate the impact of the ETS system on somes airlines in terms With this computations, taking a CO2 price equal to e14, British Airways ETS cost is about 5.6 cents per passenger carried on 100km. In average for a 1500km flight, the total price will be about e0.84. For a 4500km flight, the total cost will be about e2.52. With a CO2 price equal to e30, the cost per passenger carried on 100km is about to e0.12. The ETS impact becomes more significant again and the need of fuel efficiency crucial. It is worth noting that the average fuel consumption per tonne.kilometer of a short haul flight is always higher than a long haul flight. This is due to the aircraft performance and to the flight procedures. When we compare the real fuel consumption of a long haul flight with the average one of the airline, the extra cost for the long haul travellers is higher than it would be. For the short haul travellers the extra cost is lower. As a consequence, long haul travellers subsidize short haul travellers. Moreover, Easyjet and Iberia are really more efficient than the other airlines. The ETS impact is even positive for the low cost Easyjet.

As said before, the ETS impact depends on the fleet (type and age), the network, the type of activity (short-haul, long-haul), the load factor, the flight optimized procedures and the airline strategy. The good performance of Easyjet can for instance be explained by the youth of its fleet and its high load factor, which are easily measurable. Easyjet uses a really recent fleet with high load factors. In comparison Britsh Airways fleet is quite old and its load factor, is in average, 7% lower.

Economic model

Our model is a model of joint production in which pollution appears as a side effect of the core activity: CO2 emissions exist because airlines operate flights. This assumption is very intuitive and realistic. We will consider the case of an airline which exerts a monopoly position on a particular market. We thus voluntarily put aside the potential competition from other airlines. Our main objective in this paper is to model correctly the regulation and to evaluate the impact of this regulation on a given airline, neglecting first the effect of competition. In a companion paper (Jenvrin and Malavolti (2010)), we introduce competition and derive the effects of the regulation on competition. The total cost function of the airline is the following:

T C(q) = F C + C F (q) + X(q)
F C represent the fixed costs. All administrative costs, labour costs...are included in these fixed costs. C F (q) stand for the variable costs. To simplify the analysis, we only consider that the production variable costs are coming from the fuel consumption. The main reason is because the emissions are clearly related to the level of fuel consumption. Function C F depends on the the price of the fuel denoted p F , which is exogenous and on the quantity of tons carried q, which will be chosen by the airline. We define C f uel as a unit cost, and thus we are able to write

C F (q) = kC f uel ( q k , d), ∀k > ∀q ∈ [(k -1)q p , kq p ],
where d is the distance in km considered (exogenous) and k is an integer and q ∈ [0, q p ] with q p parameter modeling the aircraft maximum capacity for passengers (in number of tons). At this stage of the analysis, we need to give a functionnal form for the C f uel function in order to be able to be able to solve analytically the maximization of the profit of the airline. We thus use the following form

C f uel (q) = C 0 (1 + a) q
with a, a (small) positive constant and C 0 , the consumption cost for the route with all the carried staff and stuff but without passenger (the corresponding load factor is thus 0). So C 0 is linked to the basic aircraft consumption, a to the over-consumption due to passenger added (equivalent to mass added). We simplify the shape of C f uel (q, d) using Taylor series and finally obtain 2 :

C f uel (q) = C 0 (1 + aq + a 2 q2 2 ).
Function X(q) allows to take into account the cost due to the application of the ETS in aviation. X enables to compare the CO2 emissions of the aircraft with the allowances allocated to the airline for the route. Thus,

X(q) = (C F (q)ρ -R d q)p x
with C F (q) expressed in euro, ρ, a constant representing the allowance/euro spent for fuel, which depends on the fuel cost and the quantity of CO2 emitted by burning one liter of fuel.

R is the benchmark detailed in the previous section and p x represents the allowance price on the market (exogenous). We consider a linear demand P (q) = A -Bq. The variable q represents tonnes of passengers. For the airline industry, it is usually assumed that the typical demand function takes the log-linear shape. In this function the slope changes. At the initial slope, the slope is important in order to model the fact even if the price decrease it is still really high for a majority of potential customers. When the price decreases the quantity demanded becomes greater and greater. In this article we will not present the result for the log-linear demand because the syntaxically hard to present and especially the consequences of the ETS system are the same as with a linear demand.

2 More precision can be found in the appendix 1.

3 Results and consequences on airline strategies

The impact of the introduction of ETS

The airline chooses the quantity carried (expressed in "passengers in tons") q in order to maximize its profit. We compare this equilibrium solution to the one without any pollution regulation.

Proposition 1 With a linear demand, the quantity carried by the monopoly airline at the equilibrium is as follows:

q eq = k(A -aC 0 (1 + ρp x ) + 82%λc EU dp x ) 2kB + a 2 C 0 (d)(1 + ρp x )
The implementation of the ETS entails an increase of the number of passengers carried. The fuel consumption is higher and the airline profits are lower.

Proof.

We have tested the ETS impact on long haul flights, short haul flights, both with linear and loglinear demand functions. We develop below the results but the details of the method can be found in appendix 3. We studied the airline behavior in 3 different situations with different aircrafts (with different efficiency).

Parameters k, C 0 and a measure a technical impact on the equilibrium. Indeed they are all linked to the fuel consumption. They allow to take into account a technical progress that arilines may incorporated to their production system. For instance, if an airline decide to renew its fleet, its fuel consumption will be more efficient since aircraft are new and typically this corresponds to a lower C 0 and/or a lower a. Parameter k links the capacity of an aircraft to its "level of consumption". Indeed, the cost function is defined by steps in order to take into account that the capacity is not continuous. Parameters c EU and p x measure the impact of the European regulation. A "tougher" regulation would be reflected by a lower mean emission of CO2, i.e. a lower mean average fuel consumption c EU tolerated.

Besides, through the quantity of free allowances, the regulator can influence the price of an allowance p x . A tougher policy would then mean a higher price. Finally, impacts of a change of the demand from passengers are measured through parameters A (maximum of demand) and B (price elasticity): a positive demand choc means a higher A and/or a lower B. The equilibrium quantity is decreasing with the marginal production cost (a and/or C 0 ), which reflects in our case the efficiency of the aircraft in terms of fuel consumption. It is interesting to notice that if the price of the fuel exogenously increases, the equilibrium quantity decreases since mechanically the cost of producing increases (through C 0 ). Moreover, if the mean consumption per tonne-kilometer c EU used to design benchmark R increases 3 , the marginal cost also decreases. Again the quantity is higher. We show that the regulation leads to an increase of the airline activity, while its profits worsen. What are the effects at play? The introduction of the airline in the ETS means an additional cost: the airline has now to pay for its CO2 emissions. This cost is linked to its fuel consumption itself explained by its activity.

Hence, a first effect can be identified: to maintain the same level profit, the regulated airline has to reduce its activity, i.e. q eq decreases. This effect is wanted by the regulation since the reduction of activity means as well a reduction of the emissions. However, the regulation itself may induce a higher activity, through function X. Indeed, as the free credits are given as a function of the current activity, airlines have an incentives to increase their activity. More precisely, function X has two opposite effects on q eq : First, consider a situation in which, for each aircraft, the mean fuel consumption per tonne.kilometer carried is upper the "standard efficiency level", i.e. X(q eq ) ≥ 0. As a consequence, the variable cost and thus the marginal cost are higher, which pushes the ticket price upwards, and the number of passengers supplied at the equilibrium downwards. However, the way function X is defined is closely related to the fuel efficiency of the aircraft. And more precisely to the consumption per tonne.kilometer carried of the aircraft, which means that the airline would try to optimize its consumption per tonne.kilometer by optimizing the couple ("consumption","tonne carried"). That's why the load factor raises with the introduction of the ETS. The airline tries to make move closer its own consumption per tonne.kilometer to the "standard efficiency level" 82%c EU . Finally, in monopoly position the second effect is more significant and q eq becomes higher. Let us now suppose that the airline owns very fuel efficient aircraft. In this case the tax X would become a subsidy. We simulated it by improving the fuel consumption for the flight and the result is clear. When the aircraft is efficient and when c ≤ 82%c EU the equilibrium quantity increases. As X(q) ≤ 0, the two above mentionned effects are not opposite anymore: they have the similar positive impact on the supply. Indeed, here X contributes to the decrease of the marginal cost of production. Consequently, in monopoly position when the aircraft is enough fuel efficient and so X ≤ 0, the impact is clearly to raise the supply. And what if p x increases? When p x increases, the need of efficiency is more crucial for the airline.

Experimentally, the result is an increase of the equilibrium quantity. The final value of X depends on the parameters.

Investment in a more efficient aircraft

Lemma 1 Changing of aircraft for a more efficient one leads to a higher number of passengers carried, i.e. q eq is higher, a lower fuel consumption and a higher airline profit.

Proof.

See in appendix 4.

We consider an airline with a certain aircraft (non-efficient one) which copes with the ETS introduction. We study how the airline faces the legislation by two different cases. The airline keeps its inefficient aircraft compared with the airline removes its aircrafts and invests in a more fuel efficient one. The introduction of the ETS gives the right incentives in terms of renewing the fleet: the profits increase after the change of aircraft, which allows the airline to finance its investment. The gain in efficiency, i.e. the decrease of the production cost has to be sufficient. We show that, even if the airline carries more passengers, the fuel cost and then the total cost depletes.

Conclusion

At the beginning of the application, the EU will create an ex-ante benchmark "so as to ensure that allocation takes place in a manner that provides incentives for reductions in greenhouse gas emissions and energy efficient techniques, by taking account of the most efficient techniques, substitutes, alternative production processes, efficient energy recovery of waste gases, use of biomass and capture and storage of CO2, where such facilities are available, and shall not provide incentives to increase emissions"[source: European Directive]. Our study reveals the introduction of the ETS system tends to increase the airline activity: more passengers are carried at the equilibrium. This result is due to the particular shape of the ETS cost function X, which we have modelled as closely as possible from the real system. Now, airlines cope with the necessity to improve their load factor and their consumptions per tonne.kilometer. This trend will be emphasized by an increasing allowance price on the CO2 market, which is clearly expected with the entry of many sectors. We can wonder to what extent these results

are not opposite to the European Directive aim. The European goal is to deplete the total emissions of the aviation. But here, in monopoly position, we show that the equilibrium number of passengers (q eq ) is higher than without regulation. Eventually, more fuel is burnt and consequently more CO2 is emitted. However, our results show that the profits of airlines can be higher if they invest in more efficient aircraft: eventhough the activity would increase, the emissions are lower because of technical progress concerning fuel consumption.

A Appendix 1: Fuel cost function C F

In this appendix we detail the fuel cost fuel with d as distance of the route, q as tons carried and p F as fuel price parameter. C F (q, d, p F ) : fuel cost linked to the jet fuel consumption with a given aircraft and a given route expressed as e. To design this function, we define the variables and functions (F 0 (d),C 0 (d, p F ), a, q p ) which qualify the aircraft characteristics and performances. So each type of aircraft has is own four parameters.

• F 0 (d) : fuel consumption corresponding to the fuel consumption for the route with all the carried staff and stuff but without passenger (with a load-factor equivalent to 0). This function is a non-linear function, it depends on the type of haul and aircraft and it depends on the variable d, the distance covered. F 0 (d) is expressed as liter.

• C 0 (d, p F ) : consumption cost corresponding to the consumption cost for the route with all the carried staff and stuff but without passenger (with a load-factor equivalent to 0). linked with just the constant parameter p F , for ease of handling we will make appear in formulas in the rest of this part only C 0 (d).

C 0 (d, p F ) = F 0 (d) × p F Like the function F 0 (d), C 0 (d)
• a : parameter modeling the over-consumption due to an added passenger. a is not a function of d, a is a constant without unity.

• q p : parameter modeling the aircraft capacity for passengers in number of tonnes.

Besides, we define C f uel (q, d) which represents the fuel cost function of the aircraft with q ∈ [0, q p ]. We precise that we have C f uel (q, d) = F f uel (q, d) × p F with F f uel the total fuel consumption.

With a given aircraft and its fixed capacity, we can't carry more passengers than the capacity. If q > q p , to carry passengers the airline needs to use several same type of aircrafts or several times the same aircraft (the result is exactly the same). In this model, if the total demand is q and q > q p , the airline must use at least E[q/q p ] + 1 aircrafts to transport the passengers (E[q/q p ] is the entire part of q/q p ). We will consider the airline uses exactly E[q/q p ] + 1 aircrafts. So eventually we have E[q/q p ] + 1 aircrafts with the same load-factor equivalent to q E[q/qp ]+1 qp .

To determine precisely the shape of the function C f uel (q, d), we used a study realized at the ENAC (Ecole Nationale de l'Aviation Civile) and we have experimentally :

C f uel (q, d) = C 0 (d) × (1 + a) q
with a > 0 and close to 0.

Physical explication about the shape of C f uel : when a passenger is added to the flight, the airline need to add fuel because of two physical reasons. Firstly, more passengers means more on-board mass (100kg per passenger), so the aircraft mass increases and it needs more power to fly. It means a higher fuel consumption and so, more on-board fuel. Secondly, in aviation, we need to board fuel to transport the necessary fuel for the propulsion. Indeed, because of the fuel mass, the aircraft consumes fuel to transport fuel. These two physical reasons illustrate the shape of C f uel . Moreover, the parameter a is positive but close to 0. Indeed, the experience shows that additional passenger makes the necessary mass-fuel to increase but not tremendously because of the significant aircraft mass alone. We precise in the model we consider a flight without wind and in the standard flight conditions. At last, the parameters which differentiate two aircrafts with the same capacity are C 0 (d) and a. C 0 (d) is linked to the basic aircraft consumption, a to the over-consumption due to passenger added (equivalent to mass added). Finally, an airline's fuel cost is a result of two factors : the price of fuel and the fuel efficiency.

In this model, we simplify the shape of C f uel (q, d) using an equivalent. Indeed, as a > 0, close to 0 and with 0 < q ≤ q p , we can approximate (1 + a) q with the Taylor series :

(1 + a) q = 1 + n i=1 1 i! ( i-1 j=0
((qj))a i ) + o(a i ) or (1 + a) q = 1 + aq + a 2 q(q -1) 2! + o(a2)

Thereby, we choose to use the simplified shape of the cost function with q ≤ q p : C f uel (q) = C 0 × (1 + a(1 -a 2 )q + a2 2 q2)

But, experimentally we show a ≃ a(1 -a 2 ). Therefore we obtain :

C f uel (q, d) = C 0 (d) × (1 + aq + a 2 q2
2 )

The function C F (q, d) is actually a by part function. In the model, for example if q ∈ [q p , 2q p ], C F (q, d) = 2 × C f uel (q/2, d). So, we have : ∀k > 0 and k whole number, ∀q ∈ [(k -1)q p , kq p ]

C F (q, d) = k × C f uel ( q k , d)
Profit maximization We can apply the first and second-order condition to find the optimum of this function for a specific route. "Specific route" means we consider d as a fixed variable and thus we don't try to optimize the function Π with regard to d. We study : max q Π(q, d) = max q P (q)q -T C(q, d) = max q P (q)q -F C -C F (q, d) -X(q, d)

As C F (q) is a by part function equivalent to k × C f uel (q/k) on the interval [(k -1)q p , kq p ] with k whole number, we consider :

∃k ≥ 0 q eq ∈ [(k -1)q p , kq p ] Now we study

∂ (q) ∂q = A -2Bq -C 0 k( a k + a 2 q k2 )(1 + ρp x ) + Rp x d = 0 ∂2 (q) ∂2q = -2B - a 2 C 0 k (1 + ρp x ) ≤ 0
As ρp x ≥ 0, a2 ≥ 0, C 0 ≥ 0 we have ∂2 (q) ∂2q ≤ 0, so the second order condition is still checked.

At the optimum, M R = P (q) + qP ′ (q) = C ′ (q) with M R : the Marginal Revenue

A -2Bq = C 0 k( a k + a 2 q k2 )(1 + ρp x ) -Rp x d
At the optimum, when q eq ∈ [(k -1)q p , kq p ] we have q eq = k(A -aC 0 (1 + ρp x ) + Rp x d) 2kB + a 2 C 0 (1 + ρp x )

When we introduce the variable c moy with R p = 82%λc moy p x , we have q eq = k(A -aC 0 (1 + ρp x ) + 82%λc EU dp x ) 2kB + a 2 C 0 (1 + ρp x )

Airline before and after the ETS system : We consider three different airlines with three different aircrafts. We observe always the same phenomenon: the implementation of the ETS entails an increase of the number of passengers carried. The fuel consumption is higher and the airline profits are lower.

Results with an airline before and after the ETS system aircraft ac1 aircraft ac2 aircraft ac3 △ q eq tonnes 0,87 0,86 0,85 △ C F (q eq ) e 145 158 169 △ X(q eq ) e 185 700 1134 △ C T (q eq ) e 251 777 1303

△ P (q eq ) e -52 -51 -51

△ Π(q eq ) e -153 -665 -1177

△ c(q eq ) l/t.km -0,01 -0,01 -0,01 △ Load factor(q eq ) 0,02 0,02 0,02

  (2007), in which the authors emphisized the importance of having several instruments to reach good result. Our paper propose a more positive view, in examining the current regulation, trying to describe it as close as possible from reality. A paper by Hofer et al. (2009) tries to achieve the same goal with the taxation in the US. However, no economic model is presented in their paper. Finally, our work is complete the work by Albers et al. (2009) and Anger and Kholer which try to evaluate the impact of the ETS on airlines. Again, no economic model is presented which is what our paper brings.

  of cost per 100RPKs (Revenue Passenger Kilometer) considering aircraft operators would pass on most or all of the extra cost to customers. Find such a result is very interesting for two reasons. Firstly the result is more precise than a simple average amount of costs per flight. Secondly such a result enables airlines to be aware about both the real ETS cost for each route and their own efficiency in comparison with competitors. We use the reported CO2 emissions and RPKs of four airlines in 2008 and determine their average consumption per 100RPKs (passenger.100km). We choose the value of the following parameters: c EU (expressed in liters per 100RPKs), λ (expressed in tons of CO2 per liter of fuel) and p x the allowance price on the CO2 market (with two different working assumptions: 14 euros and 30 euros per ton). Our methodology is to compare the total CO2 emissions in 2008 with the allowances which would have been allocated to the airlines considering their ton.kilometers carried in 2008. Below the data (sources: Carbon Disclosure Projet 2009). We obtain the average fuel consumption per tonne.kilometer by dividing the total fuel consumption per the total RPKs carried.

  is a non-linear function and depends on the type of haul, the aircraft and the distance covered. C 0 (d) is expressed as e. As C 0 (d) and F 0 (d) are

  Above we determine the extra c mean expressed as l/100RPKs, which is the difference between the real emissions and the allowances given free of charge. Then, we are able to compute the extra quantity of fuel which is burnt with respect to the EU standard efficiency level of consumption for each passenger carried on 100km.ETS cost for ailines with carbon price p 1Airlines Extra cost in e/100RPKs Total cost in e

		Airlines performances ETS cost for ailines with cabon price p 2
	Airlines	Rpk000	Emi.2008 (tonnes) Fuel cons.(liters) cmean (l/100RPKs)
	Easyjet 49077231 Easyjet	4307000 -0.052	1709126984 -25 952 180	3.482
	Air France-KLM 162658000 Air France-KLM	27506144 0.191	10915136508 310 926 088	6.710
	British airways 115770579 British airways	16840627 0.120	6682788492 139 199 473	5.772
	Iberia 52845795 Iberia	5839469 0.015	2317249603 8 107 227	4.384
			Exogeneous data
		c EU ET S (l/100RPKs)	5.1
			82%c EU ET S	4.182
			λ (T C02 /L) 0.00252
			CO2 price p 1	e14
			CO2 price p 2	e30
		Extra consumption for airlines
		Airlines Extra cmean (l/100RPKs) Extra kgCO2/100RPKs
		Easyjet	-0.699	-1.762
	Air France-KLM	2.528	6.371
	British airways	1.590	4.008
		Iberia	0.203	0.511
		Airlines Extra cost in e/100RPKs Total cost in e
		Easyjet	-0.024	-12 111 017
	Air France-KLM	0.089	145 098 841
	British airways	0.056	64 959 754
		Iberia	0.007	3 783 372

The exogenous value c EU ET S is based on the "Global Market Forecast 2009-2028" published by Airbus. Given that this value will be designed by the EU with respect to a certain percentage of the aviation emissions of

2004, 2005, 2006

, we choose to take c EU ET S = 5.1l/100RPKs. Obviously, all the scheme and its consequences are calibrated by this value.

We consider that even in a monopoly on this particular route we consider, our airline fuel consumption effect is negligeable.

project financed by the CLEANSKY consortium, www.cleansky.org

A Appendix 2: Detail of parameters and method

We detail below all the exgeneous values we used in our model. There are two types of constants. Some are linked to the type of aircraft used, some others not. We based our model on a San Fransisco-Paris flight. In our study of the ETS impact on an airlines which doesn't change its aircraft, we simulate for three aircrafts (ac1, ac2, ac3) with as parameters

Constants unlinked to the type of aircraft

Type of aircrafts

Constant ac1 ac2 ac3

Basis Consumption C 0 1.1C 0 1.2C 0 Over-consumption due to an added passenger a a a

Remark : We consider the parameter a (parameter modeling the over-consumption due to an added passenger) is similar for the three aircrafts.

Airline before and after the ETS with a more efficient aircraft :

We compare the two following situations: -An airline with the aircraft ac2 which changes its aircraft with introduction of the ETS system -An airline with the aircraft ac2 which doesn't change its aircraft with introduction of the ETS system We observe: changing of aircraft for a more efficient one leads to a higher number of passengers carried, i.e. q eq is higher, a lower fuel consumption and a higher airline profit.

Results with an airline before and after the ETS system with a more efficient aircraft ac1 with ETS -ac2 without ETS ac2 with ETS -ac2 without ETS △ q eq tonnes 1 0,86 △ C F (q eq ) $ -5905 158 △ X(q eq ) e 251 620

△ C T (q eq ) e -5800 777

△ P (q eq ) e -61 -51

△ Π(q eq ) e 5921 -665

△ c(q eq ) l/t.km -0,05 -0,01 △ Load factor(q eq ) 0,02 0,02