2005・37

Strategic Alliance versus Competition:
Airlines’ Choices and their Impact on Economic Welfare
Hideki Murakami

Strategic Alliance versus Competition:
Airlines’ Choices and their Impact on Economic Welfare

Hideki MURAKAMI
Graduate School of Business Administration
Kobe University
2-1 Rokkodai-cho, Nada-ku, Kobe, 657-8501, JAPANTel : +81-78-803-6941 Fax: +81-78-803-6969
E-mail: hidekim@kobe-u.ac.jp

Abstract
This paper theoretically analyses the duopolistic behavior of two hypothetical airlines operating in afour-point hub-and-spoke route network system, and examines the impact of this behavior on economic welfare.

The important character of these two airlines is that they are of different (i.e., asymmetric) cost structures andproducts. The main findings are that (1) in rare cases, two asymmetric airlines might form a strategic alliance,and (2) Cournot competition is much more likely to generate economic welfare than a strategic alliance.

However, in some cases in which the degree of economies of density is sufficiently small, two firms may engage

in Cournot competition, despite the fact that strategic alliance generates greater economic welfare. Therefore,

the degree of economies of density is the key factor to which governments should attend.

Keywords: Airlines with asymmetric structure, Two-stage duopolistic game, Economies ofdensity, Cost complementality, Economic welfare

11. Introduction

Since the mid-1980s, many countries have experienced a liberalization of international markets by

accepting the US open-sky policy. International air markets have been tightly regulated in terms of setting

airfares, flight frequency, the designation of airlines, the choice of alliance partners and so on. Since many

countries still tightly regulate the use of fifth freedom rights among each other, each airline cannot build theiroptimal route networks.

In order to overcome these legislative operational restrictions, a domestic airline sometimes lobbies

for strategic alliance with a foreign airline. Such alliances are of two types: deep- and shallow-type. The former

allows two airlines to agree on setting the same ticket price, the control of departures, the mutual holding ofequities, and/or code-sharing. This type of strategic alliance requires antitrust immunity from their countries.

The shallow-type alliance, on the other hand, does not require government approval, since the airlines are notregarded as forming a cartel. Rather, the two airlines simply agree on the coordination of operations and/or

issue through-tickets on a route-by-route basis.

This paper analyses the economic effects of strategic alliance between airlines by introducing theconcept of an “asymmetric firm structure”. We define an asymmetric firm structure as the alliance of two firmsthat are asymmetric with respect to their cost structure and their products. In other words, one airline is assumed

to be a low-cost carrier, while the other is the high-cost network carrier, and they produce differentiatedproducts.

2

In order to see the effects of an alliance on economic welfare, we usually consider the ticket pricelevel, output level, cost level and efficiency of production. The ticket price level is normally affected by the

degree of competition, which in turn is dependent on the strength of barrier to entry. There have been many

empirical and theoretical studies on entry behaviors and inter-firm rivalries, including the works of Bresnahan

and Reiss (1990), (1991), Berry (1992), Brandar and Zhang (1990), (1993) and Oum et al. (1993). As for airline

costs, Caves et al. (1984) introduced the idea of economies of density, and empirically showed that this concept

was a significant factor in the economics of airline industries. Brueckner and Spiller (1991), (1992), and Zhang(1996) stress the importance of cost complementarities in airline networks. Due to cost complementarities, thedecrease in output due to competition in a hypothetical route (A) may raise the level of marginal cost of route(B) which is adjacent to (A). Oum, Park, and Zhang (1996) and Park (1997) apply the concept of economies ofdensity and cost complementarities in a network to the analysis of strategic alliances between airlines ininternational markets.

These analyses assume that the firm size is symmetric and airlines produce homogeneous products.

However, based on our observations of the operations of Southwest Airlines and Jet Blue in the US and Ryan

Air in Europe, low-cost airlines have played important roles in both international and domestic air markets. In

marked contrast to the US mega-carriers, these low-cost airlines have not developed huge hub-and-spoke routesystems, computer reservation system, or frequent flyer programs. Although many researchers insist that

efficient route systems and customer-binding strategies are vital for the survival and continued competitivenessof airlines, these lower-cost airlines have actually survived without these devices. To elucidate the mechanism3

of this survival, this paper aims to analyze the behaviors of two airlines with asymmetric cost structure anddifferentiated products.

Schmalensee (1987) and Mason and Nowell (1992) previously analyzed the duopoly competition

between firms of asymmetric firm size (i.e., firms of different cost structures). Schmalensee contends that if a

firm has sufficient cost advantage over its rival, mutual profits generated by competition might exceed the profit

generated by collusion.

Mason and Nowell demonstrate that two asymmetric firms tend to conduct

non-collusive behaviors and require a longer period of time to reach market equilibrium than would twosymmetric firms. This paper will attempt to apply these concepts of the asymmetric firm structure to theanalysis of a duopolistic airline model.

Section two explains the route systems assumed in this study, as well as the properties of low- andhigh-cost airlines. Section three explains the incentives for low- and high-cost airlines to agree or disagree withcollusive behavior (i.e., the strategic alliance) using the two-stage game framework, and also analyses how

agreement between two asymmetric airlines on strategic alliance or Cournot competition affects price, output,

profit and economic welfare.

The main findings are that (1) in rare cases, two asymmetric airlines might form a strategic alliance,and (2) Cournot competition is much more likely to generate economic welfare than a strategic alliance.

However, in some cases in which the degree of economies of density is sufficiently small, two firms may engage

in Cournot competition, despite the fact that strategic alliance generates greater economic welfare. Therefore,

the degree of economies of density is the key factor to which governments should attend.

4

Section foursummarizes the findings of this paper.

2. Route Systems, Profit Functions, and their Relevant Properties

Figure 1 shows the hypothetical “pre-entry” route system.

Ａ

Ｃ

Ｂ

H

Figure 1. Pre-entry route structure

Firm 1, the high-cost-incumbent network carrier, serves three airports within a rectangular area:

airports A, H, and B. There is traffic flow between A-H and H-C, and these two routes are connected by directflights. There is also traffic flow between A-B, but there are no direct flights. Firm 2, the low-cost airline,

serves two airports within a circular region: airports B and C. Firm 2 intends to enter the H-B market, which we

assume has more traffic than any other route.

The next assumption concerns the “post-entry” route system. Figure 2 shows the situation in which

Firm 1 and Firm 2 form a strategic alliance under which they agree on the share of joint profit, the proximity of

their ticket counters, and the coordination of departures and baggage handling. Due to this alliance, new traffic

flow is generated between A-C, but there is no direct flight between them. Passengers moving between A-C

must change planes at hub H and/or hub B. New traffic flow is also generated between H-C, but since there is no5

direct flight, passengers must change planes at airport B.

Ａ

Ｃ

Ｈ

Ｂ

Figure 2. Route structure after the strategic alliance

Figure 3 shows the route system after Firm 2 has entered and the two firms initiate Cournot

competition between H-B. This competition inevitably has an impact on the markets of routes A-B and H-C.

Passengers traveling routes A-B and H-C can choose either the H-B flight offered by Firm 1 or that offered byFirm 2 depending on the level of air-ticket prices. In this case, neither Firm 1 nor Firm 2 provides seamlessly

connected services at either hub H or hub B, so passenger flow between A-C is assumed to be zero.

Ａ

Ｃ

Ｈ

Ｂ

Figure 3. Route structure under duopolistic competition

Under the assumption shown in Figure 3, the profit function of Firm 1 and Firm 2 can be written as

follows.

6

1
1
2) + Q1AB D(Q1AB ) − c(Q1AH + Q1AB ) − c(QBH1 + Q1AB )π 1CO = Q 1AH D(Q 1AH ) + Q BH
D (Q BH+ Q BH(1)2
1
2) + QBC2 D(QBC2 ) + QHC2 D(QHC2 ) − C (QBH2 + QHC2 ) − C (QBC2 + QHC2 )π 2CO = QBH
D(QBH
+ QBH

(2)

On the other hand, under the assumption that Firm 1 and Firm 2 form a strategic alliance and agree to

share

their

profits

equally,

theirprofitfunctionscanbewrittenasfollows.

12
π 1 AL = π 2 AL = [Q 1AH D(Q 1AH ) + (QBH
)D(QBH1 + QBH2 ) + Q1AB D(Q1AB ) + QBC2 D(QBC2 )
+ QBH

1
2
2
2
1
+ QHC D QHC + Q 1AC+ 2 D Q 1AC+ 2 − c Q 1AH + Q 1AB + Q 1AC+ 2 − c QBH+ Q 1AB + Q 1AC+ 2

(

(

−C Q

2
BH

) (

+Q

2
HC

) ( ) (+ Q ) − C (Q + Q
1+ 2
AC

2
BC

2
HC

+Q

1+ 2
AC

) (

)]

)

(3)

Economic theory assumes the properties of cost function: they are homogeneous degree one, concave(to be checked by seeing whether the Hessian matrix of each cost function is negative definite) andnon-decreasing in input prices. In addition, this paper imposes the following assumptions following previous

studies.
（A）

（B）

（C）

∂c
∂C
> 0 (i = AH , BH , AB) 、> 0 (i = BH , BC , HC )
1
∂Qi
∂Qi2
∂ 2c

< 0 (i = AH , BH , AB) 、
2

( )

∂ Qi1

∂ 2C

( )

∂ Qi2

2

< 0 (i = BH , BC , HC )

∂ 2c
∂ 2C
<
0
(
i
,
j
=
AH
,
BH
,
AB
,
i
≠
j
)
、
< 0 (i, j = BH , BC , HC , i ≠ j )∂Qi1 ∂Q 1j∂Qi2 ∂Q 2j( ) ( ) ∀ Q = Q (i = BH , BC , HC（D） C Qi < c Q j
2

1

2
i

1
j

j = AH , BH , AB )Assumptions (A) and (B) mean that economies of density are effective in an airline industry. Theseassumptions are also made by Caves, Christensen, and Tretheway (1984) and Gillen, Oum, and Tretheway(1990). Assumptions (A) and (C) mean that the cost complementarities exist. Assumption (Ｄ) means that the

total cost of Firm 2 is always lower than that of Firm 1. In addition, this paper follows the assumption by

7

Brueckner and Spiller (1992), Zhang (1996), and Park (1997) that the marginal cost of an airline is linear andslopes downward:

MC 1 = 1 − θQ1(4)

MC 2 = φ − θQ 2

(5)where θ > 0 and 0 < φ < 1 . The positive sign of θ and 0 < φ < 1 are the restatement of assumption (A)and (B) (that is, the existence of economies of density), and (D) (asymmetric cost structure).

Next, since this paper assumes that two airlines produce differentiated products, our inverse demand

functions are written as follows.
1
1
2
PBH
= α1 − β1QBH− γQBH

(6)

2
2
1
PBH
= α 2 − β 2 QBH− γQBH(7)

where α 1 > 0, α 2 > 0, β 1 > 0, β 2 > 0 , and assuming that two airlines are substitutes for passengers, γ > 0
and normally β 1 > γ > 0 and β 2 > γ > 0 . For convenience, let β 1 be unity and let β 2 be denoted asjust β and not equal unity. This transformation does not lose the generality of analysis. In addition, since thispaper assumes that the market B-H is larger than any other route, it is necessary to parameterize this assumption.

Without losing the generality, this paper assumes that route B-H is 50% as large as A-H, B-C, A-C, A-B and

H-C, and competition in B-H does not affect either A-H or B-C (that is, the demand functions of A-H and B-C

do not shift due to the competition in B-H, while those of A-B and H-C do). Our demand functions can now be

rewritten as follows.
1
1
2
PBH
= 3α 1 − QBH− γQBH

8

(8)

2
2
1
PBH
= 3α 2 − βQBH
− γQBH(9)

The demand functions of other routes are:(i = AH , AC )Pi1 = 2 − Qi12PBC=(2 − Q )
β
1

2
BC

1
PAB
= 2α1 − Q1AB

2
PHC
=

(2α − Q )
β
1

2

2
HC

If Firm 1 and Firm 2 form a strategic alliance, the demand function of route B-H is derived byhorizontally adding up each demand function. In this case, δ is zero and α = α 1 = α 2 .
1+ 2
1
2
PBH
= 3α − QBH− βQBH

Now we have a total of six parameters in each profit function: they are, α 1 , α 2 , β , γ , φ , and θ . In
order to avoid complexity, it is convenient to define these parameters using real numbers. Since this paper isinterested in the competition between firms with asymmetric cost structure, We choose real numbers forparameters β , γ , and φ such that two firms are (1) almost symmetric and (2) very asymmetric.
① β = 1.1, γ = 0.9, φ = 0.6 (almost symmetric)② β = 1.5, γ = 0.5, φ = 0.5 (very asymmetric)

In addition, we must impose restrictions on the demand and cost functions of B-H, and should also consider

the non-negative conditions of price and output. Considering all these properties and restrictions, we finallyobtain the following binding conditions for θ . From ①, we have the conditions that 0.2730 < θ < 0.2923
and from ②, 0.2689 < θ < 0.3138 .

9

3. Economic Analysis of the Behaviors of Asymmetric Firms

This paper considers the following two stage game: at the first stage Firm 2 invests for entry andadvertises itself to shift the demand upward, and at the second stage both firms either engage in Cournot

competition or choose a strategic alliance. If the equally shared profit from alliance is greater than the profit

from competition, each firm is assumed to choose to agree on the strategic alliance and vise-versa. This paper

also refers to the status of the competition by deriving the strategic effect and the effect on the rival’s profit

following the framework of Tirole (1988). The strategic effect refers to the manner in which the advertising

investment of Firm 2 upon entry affects its own profit via the effect on the output of its rival. The effect on the

profit of its rival is straightforward: i.e., the manner in which the advertising investment of Firm 2 affects the

profit of Firm 1. If the advertising investment of Firm 2 has negative effects on its own profit and on the profit

of its rival (a situation referred to as a “puppy dog strategy”), Firm 2 would refrain from choosing large

investment, and both firms would initiate negotiations toward a strategic alliance. However, if the advertising

investment of Firm 2 has a positive strategic effect on its own profit and a negative effect on the profit of its rival(a situation referred to as a “top dog strategy”), Firm 2 would continue to compete in order to increase its profit.

Table 1 relates Tirole’s framework with the stability of alliance.

Table 1 states that if both the strategic effect on the profit of Firm 2 and the strategic effect on the

profit of its rival are positive (a “fat cat strategy”), both firms will continue the competition. If the strategic10

effect on its own profit is negative and the strategic effect on the profit of its rival is positive, Firm 1 willcontinue to compete while Firm 2 will seek to cease competition.

Strategic effect on its own profit

Effect on rival’s profit

Status of competition+-

Unstable++

Continued-+

Unstable--

Would be ceased

Table 1. Tirole (1988)’s framework and the status of competition

We can obtain the solution of this two-stage game by solving the subgame perfect Nash equilibrium atthe second stage; then, by using the solutions at the second stage, we can solve the optimization problem at thefirst stage. At the first stage, Firm 2 must invest in advertising, but when it agrees on alliance, it can advertise

jointly with Firm 1, while if it chooses to compete it must pay all the advertising costs. Therefore, it is natural toassume that Firm 2 will invest more on advertising when it competes than when it agrees on alliance. For

convenience, we will consider the investment when Firm 2 agrees on alliance to be KAL

= 0.25 , and thatwhen it denies strategic alliance to be K = 0.75 .
c

The important relationship between the investments in advertising and the demand function is that theadvertising investment of Firm 2 always shifts the demand function upward. However, it is important toconsider whether the advertising investment of Firm 2 at the first stage increases the whole market demand or
only its own demand. Depending on whether we set the condition α 1 ≠ α 2 or α = α 1 = α 2 , we might*obtain different results in regard to the strategic effect on the profit of Firm 2 and the effect on its rival (i.e., Firm

11

1).

(a) The profit of Firm 1 and Firm 2 when two firms are of almost symmetric structure{ β = 1.1, γ = 0.9, φ = 0.6 }Solving the two-stage game, we have obtained the following relationship between the profit fromalliance (denoted as πiAL

(i = 1,2) ), the profit from Cournot competition ( π iCr (i = 1,2) ) and α (see Figure4). In this case, we assume that the advertising investment of Firm 2 at the first stage increases the whole(demand in the markets B-H, A-B, and H-C dα*

dK > 0, α * = α 1 = α 2 ) .

π 2 AL < π 2Cr ∀ {θ : (0.273,0.292)}

π1AL > π1Cr ∀ {θ : (0.273,0.292)}

π 1 AL < π 1Cr ∀ {θ : (0.273,0.292)}

π 2 AL > π 2Cr ∀ {θ : (0.273,0.292)}

0.979

0.999

1

1.174

α*

1.212

Figure 4. The relationship between πiAL, π iCr , and α *when two firms are of almost symmetric structure

We assume that the initial value of α is unity and dα**

dK > 0 . Therefore, we are interested inonly the shaded area. In this area, the profit of Firm 2 from Cournot competition always exeeds the profit fromthe strategic alliance. However, the relationship between π

1 AL

and π

1Cr

is quite dependent on the value of θ(i.e., the degree of economies of density) when 1.174 < α < 1.212 , and when α is larger than 1.212, the**profit of Firm 1 from Cournot competition is always larger than its profit from the strategic alliance. On theother hand, when α is smaller than 1.174, the profit of Firm 1 from Cournot competition is always smaller*12than its profit from the strategic alliance. Therefore, in this situation the behavior of Firm 1 is dependent on the

degree of upward shift and the degree of economies of density, while the choice of Firm 2 is quite

straightforward: it always prefers Cournot competition.

(b) The profit of Firm 1 and Firm 2 when two firms are of very asymmetric structure{ β = 1.5, γ = 0.5, φ = 0.5 }On the other hand, when two firms are of very symmetric structure, the results are in marked contrast

to the case of almost symmetric structure: the profit of Firm 1 from Cournot competition is always larger than its
profit from strategic alliance when α > 1 (Figure 5).
*

π

2 AL

>π

2Cr

π 1AL < π 1Cr ∀ {θ : (0.269,0.314)}∀ {θ : (0.269,0.314)}

π 1AL > π 1Cr ∀ {θ : (0.269,0.314)}

0.947

π 2 AL < π 2Cr ∀ {θ : (0.269,0.314)}

0.985

1

1.054

Figure 5. The relationship between π

α*

1.084
iAL

,π

iCr

, and α*when two firms are of asymmetric structure.

Firm 2 will prefer to offer strategic alliance when its advertising at the first stage does not increase themarket demand very significantly ( 1 < α < 1.054 ), but when the intercept of market demand curve increase*

more than 8.4%, the two firms will initiate Cournot competition. When 1.054 < α < 1.084 , Firm 2 will*

prefer either strategic alliance or competition depending on the degree of economies of density. In this range,

because]the density works more strongly, Firm 2 will prefer competition. Generally speaking, competition13

might occur more easily when the two firms are of very symmetric structure than when the two firms are ofalmost symmetric structure.

(c) The Characteristics of Competition between Two Firms of Asymmetric Structure

According to the results in 3(a) and 3(b), it is very unlikely that two firms that have asymmetricstructure will agree on the strategic alliance regardless of the degree of asymmetry. Even when the demand

curve shifts upward just slightly, either of the firms would deny the strategic alliance. Our next question, then,would concern the type of Cournot competition to be conducted, and whether or not this competition would be

likely to continue.

The effects of the advertising investment of Firm 2 on its own profit via the outputs of its rival(strategic effect) and the effects of the advertising investment of Firm 2 on the profits of its rival are shown in

Table 2.
When α = α 1 = α 2*Almost symmetric case

Asymmetric case

Strategic effect on its own profit

9 2 ∂Q
− QBH
10
∂α

dα
<0
dK

1
dα *
1 2 ∂QBH− QBH<02∂α * dK

Effect on rival’s profit2
9 1 ∂QBH
dα *
<0
− QBH
10
∂α * dK2
1 1 ∂QBH
dα *
<0
− QBH
2
∂α * dK

Almost symmetric case

Asymmetric case

9 2 ∂Q dα 2
− QBH
>0
10
∂α 2 dK1
dα 2
1 2 ∂QBH− QBH>02∂α 2 dK2
dα 2
9 1 ∂QBH
− QBH
>0
10
∂α 2 dK2
dα 2
1 1 ∂QBH− QBH>02∂α 2 dK

When α 1 ≠ α 2Strategic effect on its own profit

Effect on rival’s profit

1
BH
*

*

1
BH

Table 2. Results of the strategic effects on the profit of Firm 2
and the effects on the profits of its rival

14

When α = α 1 = α 2 , the advertising investment of Firm 2 would decrease its own profit, and thus*

Firm 2 is unwilling to make a large investment at the first stage. If Firm 2 refrains from large investment, this isgood news for Firm 1, because the effect of investment on the profit of the rival is negative. Therefore, theadvertising investment of Firm 2 increases the whole market demand, Firm 2 will refrain from large investment,

and will not compete aggressively regardless of the degree of asymmetry. It might also be said that when Firm

2 expects that demand will increase only slightly, it will not enter a B-H market when two firms are ofasymmetric structure.
However, when α 1 ≠ α 2 (in other words, when Firm 2 succeeds in increasing its own demand byinvestment in advertising), Firm 2 will take a “top dog” strategy: it will try to drive its rival out of the market byaggressive investment in advertising, which might be an important business strategy for Firm 2 to bind its own

customers. In this case, we expect that very fierce competition would be conducted in route B-H.

(d) Prices, Outputs, and Economic Welfare

Finally, we will investigate how the prices, outputs, and economic welfare would be affected by

Cournot competition. Table 3 shows the price and output in each market. The price-output sets when two firms

form strategic alliance are also shown. The degree of economies of density is set at 0.28 (medium value).

In the almost symmetric case, the total traffic volume (the vertical sum of outputs) as aresult of Cournot competition is 4.87 when the intercept of the market demand curve increases by15

10%. When the two firms form a strategic alliance, the total traffic volume is 4.86, so the traffic
volumes for both the two cases are almost the same. The weighted average of the price is 1.21 asa result of Cournot competition, while it is 1.34 as a result of the strategic alliance. The reason
why the monopolistic traffic volume does not differ substantially from the volume of thecompetitive case is that the new market A-C is created in the monopolistic case. However, it isapparent that competition would reduce the average price level, and thus that consumer surplus
would increase.

AlmostSymmetric

Case

Asymmetric(θ = 0.28)
Price, Output

1
AH
1
AB

P ,Q
P ,Q

1
AH
1
AB

2
2
PBC
, QBC

2
2
PHC
, QHC

1+ 2
PAC
, Q1AC+ 2

Alliance

Case(θ = 0.28)

Cournot

Cournot(

Alliance

Cournot

Cournot(α = 1 )α = 1 .1 )(α = 1 )( α = 1 .1 )1.25, 0.75

1.38, 0.62

1.35, 0.65

1.34, 0.66

1.37, 0.63

1.34, 0.66

1.42, 0.58

1.75, 0.25

1.78, 0.42

1.69, 0.31

1.69, 0.31

1.71, 0.49

0.99, 0.92

1.07, 0.85

1.24, 0.87

1.06, 0.63

1.08, 0.61

1.07, 0.62

1.10, 0.82

1.10, 0.82

1.14, 0.96

1.15, 0.57

1.14, 0.57

1.20, 0.66

1.53, 0.47

1.83, 0.17

1
1
PBH
, QBH

1.40 0.65

1.15, 0.79

1.62, 0.98

1.70, 1.16

2
BH
1+ 2
BH
1+ 2
BH

1.25, 1.07

1.00, 1.18

1.31, 0.80

1.39, 0.88

P ,Q

2
BH
1
BH
2
BH

P

,Q

1.67, 1.26

1.74, 0.61

P,Q

1.67, 0.06

1.74, 0.43

Table 3. Price and output in each market as a result of competition and allianceIn the asymmetric case, the total traffic volume as a result of Cournot competition when demand shifts

upward by 10% is 4.47, and even if we assume that the market demand curve does not shift upward, the traffic

16

volume is 3.90. On the other hand, the total traffic volume as a result of the strategic alliance is only

3.38,despite the fact that a new market A-C is created. The weighted average price is 1.42 as a result of Cournot

competition with a 10% increase of the intercept of the demand curve, while it is 1.44 as a result of alliance. The

average price level of the Cournot case is slightly lower than that of the alliance case, but if the output increases

significantly, the consumer surplus would apparently increase through competition.

What then, would be the status of the total economic welfare? In order to examine this, this sectionjderives the total economic welfare ( W ) using the following formula:6

W j = π 1 j + π 2 j + ∑ CS i j(i = AH , AB, BH , HC , BC , AC

j = AL, Cr )

i =1

j

where CS i is the consumer surplus of each market. This is easily computed, since this paper assumes a linear
demand function.
In both the asymmetric and almost symmetric cases, the total economic welfare from Cournot

competition ( WCr) is always greater than that from strategic alliance ( WAL) regardless of the degree of

economies of density, as long as the intercept of the market demand curve shifts upward by more than 10.8%. If

the demand curve shifts upward by less than 10.8%, whether or not W

Cr

is greater than W

AL

is dependent on

the degree of economies of density. The more effective the operation of the economies of density, the more

likely it is that W

Cr

>W

AL

. In this case, it might happen that two firms engage in Cournot competition eventhough strategic alliance generates greater economic welfare. Such a case might occur when the economies ofdensity is small (around 0.275-0.285). In this case, it might be better for the government to recommend that thetwo firms agree on a strategic alliance, although this case might happen less frequently than that in which17π 1Cr > π 1 AL , π 2Cr > π 2 AL and W Cr > W AL occur simultaneously.

4. Summary of Findings

The present theoretical analyses have revealed the following.

(1) When two firms are of almost symmetric structure, the low-cost airline (Firm 2) will consistently

prefer Cournot competition, while the high-cost airline (Firm 1) might not do so, unless the market

demand curve shifts upward very significantly that is, by more than 21%.

(2) When two firms are of asymmetric structure, the high-cost airline (Firm 1) will consistently prefer

Cournot competition, while the low cost airline (Firm 2) might be reluctant to do so. However, if themarket demand curve shifts upward by 8.4% due to advertisement by the low-cost carrier, the low-costairline will also prefer to compete. Therefore, Cournot competition will be more likely to occur when

the two firms are of asymmetric structure than when they are of almost symmetric structure. This

result is consistent with the discussions by Schmalensee (1987) and Mason and Nowell (1992).

(3) In both cases, the low-cost airline would invest in advertising very aggressively to defeat its rival only

when it can bind its own customers. If it fails to bind them, the low- cost airline would not invest on

advertising very aggressively because the investment would decrease its profit.
(4) The situation in which π

1Cr

>π

1 AL

,π

2 Cr

>π

2 AL

and W

Cr

>W

AL

is likely to occur as long as theadvertising investment of the low-cost airline pushes the market demand curve upward by more than18

10.8%. However, when the degree of economies of density is sufficiently small, it might happen thattwo firms engage in Cournot competition even though a strategic alliance would generate greater

economic welfare. Therefore, the degree of economies of density is the key factor to which thegovernment should attend.

[2005.10.6 727]
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