Spinning off low cost carriers��when it does make sense?

Ying Kong

ABSTRACT

In the last 10 years, a number of major and flag-bearer air carriers have been spinning off low fare alternative airlines from their main operation to compete with low fare rivals. This paper examines the incentives and possible indicators of success for this strategy. Using a two-stage game model, we determine that the high fare airline company will find it profitable to create its own low fare airline when (a) the factor of cross elasticity between high fare good and low fare good is relative large and (b) the existing load factor on the high fare airline is relatively high. The model also shows that total welfare as a result of this strategy can rise under some favourable conditions.

1. INTRODUCTION

"Lets face it, if you're an airline and your name doesn't begin with Southwest, you are by default a bankruptcy candidate." Jamie Baker, an airline analyst at J.P. Morgan, to The Associated Press on the restructuring going on in the airline industry.

To be fair, Jet Blue Airways, Airtran and West Jet, the disciples of Southwest Airlines, are also profitable North American airlines. Not coincidentally, all of these share common characteristics--they are all no-frill low cost point-to-point airlines. The Southwest airline case study is quickly filling up textbooks, journals and magazines as the new airline model for profit maximization. The impact of Southwest on the airline industry has been estimated at $12.9 billion in savings to consumers (1).

All airlines have four broad components in their profit functions; the product of yield and traffic equates to revenues and the product of unit costs and output equates to costs. Southwest Airlines has focused primarily on reducing unit costs to increase traffic through the lowest prices. There are five key elements in their strategy. First, utilize all the same aircraft (737s) to reduce training and maintenance costs. Second, use less expensive secondary airports near major centers to reduce transaction cost laden turnaround times and increases productivity. Third, pay high attention to customer satisfaction to increase load factors (2). Fourth, reduce booking costs through an aggressive Internet strategy. Finally, maintain lower labor costs by more closely aligning interests between labor and management (3) (Holloway, 1997).

In contrast to Southwest and its clones, a large segment of the North American airline industry is in financial free fall. Air Canada filed for bankruptcy on April 1st, 2003 to join Hawaiian Airlines and United. American Airlines reduced its costs by $1.6 billion on March 31st to just avoid bankruptcy. U.S. Airways just finished reducing its costs while under bankruptcy protection (4). Delta and Northwest are using the examples of American and US Airways as leverage for reducing costs.

There are numerous explanations for the financial crisis facing most of the North American major and flag bearer carriers. There are exogenous factors reducing traffic such as health and security concerns. There are also a number of endogenous factors relating to their comparatively high per unit costs. At this stage, the question facing the North American major and flag bearer carriers is not whether they should compete with Southwest, WestJet and other low cost carriers by reducing their costs, but how to do it and quickly.

A Consumers including business travelers are buying down and this trend is permanent. The days when CFO=s issued directives not to travel in executive class have been replaced by new directives to only travel with low cost carriers whenever they are available. We have to conform to this reality and transform Air Canada into a low cost carrier in its own right. We cannot product a product for $1 and sell it for 754 while our main domestic competitor can produce the same product for 504.@ B Robert Milton, President of Air Canada, in the National Post, March 22nd, 2003.

A number of broad cost cutting strategies have emerged (Holloway, 1997). Most of these strategies are directed at managing specific internal cost drivers. For example, as discussed above, a number of airlines are using a combination of threats based on exogenous factors and bankruptcy to gain significant concessions from labor, creditors and suppliers. Other airlines are reducing output and cutting back on routes. United Airlines just cut back a number of routes, as did KLM. Strategic alliances such as those by Northwest, Delta and Continental are being used to achieve efficiencies in ticketing and bulk purchases (Oum, Park and Zhang, 2000).

Beginning in the early 1990s, a new cost management strategy, called the spin off strategy, emerged. A number of new airlines were established either within but separate from the main airline or as standalone entities. These include Continental Lite in 1993, Shuttle by United in 1994, Delta Express in 1996, and Air Canada=s Tango and Zip in 2001 (6).

All of these new airlines were intended to directly compete with low cost point-to-point Southwest type carriers and contribute either revenues or increased traffic to their parent companies. In theory, they would lower costs by adapting as much of the Southwest model as possible. In some point-to-point markets, the existence of these low cost spin offs would provide an effective barrier to entry, and in others; they would directly compete with Southwest and/or its followers.

This strategy is not without some obvious risks. First, there is the selection of the appropriate point-to-point markets to compete over. Second, there is a branding issue and possible confusion and alienation among customers (7). Third, it is possible that the client base from the mainline is merely siphoned off to their upstart. Fourth, there is a shift in corporate culture required to dramatically reduce costs per unit. In other words there are high switching costs. Finally, there may be problems satisfying premium passengers who are forced to use the discount service (8).

The results so far indicate that this strategy is not working well in North America. Continental Lite stopped operating in 1996 after reporting over $100 million in losses in 1994. United Express suspended its operations in 2001 because its costs were not significantly different from the parent company. A plan to re-launch Delta Express using a different name and different cost structure was announced in 2002 (Washington Times, Nov. 16th, 2002).

The practical experience of others has not daunted Air Canada and still has support among the business community (9). Is this strategy viable? (10) When or under what conditions the airline companies should practice this strategy? The objective of our paper tries to use economic model to answer these questions. The paper uses a two stage game theoretic model to generate the parameters that an optimizing Air Canada or similar major airline should consider in choosing where and how to spin off a no frill carrier to compete with a low cost alternative. Chief among these parameters are the cross elasticity of demand in various markets and the load factor.

The remainder of the paper is organized into three sections. Section 2 presents the basic model. Section 3 examines main airlines with and without concurrent production of low fare substitutes. Section 4 concludes. Several technical derivations are relegated to an Appendix.

2. BASIC MODEL

We assume that there are two goods in the market; a high fare good ([X.sub.h]) and a low fare good ([X.sub.l]). In a compromise between generality and tractability, we assume that consumers possess identical quadratic utility functions yielding satisfaction from consumption of a high fare good in quantity [X.sub.h] and from its substitute (the low fare good) in the amount [X.sub.l]. Then:

(1) U = [X.sub.0] + u([X.sub.h], [X.sub.l] = [X.sub.0] + [[alpha].sub.h][X.sub.h] + [[alpha].sub.l][X.sub.l] - [1/2]([beta][X.sup.2.sub.h] + 2y [X.sub.h][X.sub.l] + [[beta].sub.l][X.sub.l.sup.2])

where [X.sub.0] reflects the utility derived from a competitive numeraire sector, [[beta].sub.h] >0, [[beta].sub.l] >0, y >0 and [y.sub.2] < [[beta].sub.h][[beta].sub.l] to ensure convexity.

From (1) can be derived linear inverse demand relations:

(2) Pi = [differential]U/[differential]Xi = [alpha]i - [[beta].sub.i] - Xi - Y Xj, i, j = h, l; i [not equal to] j

(3) Xi = 1/[[beta]i [beta]j - [y.sup.2]][([alpha]i - Pi)[beta]j - ([alpha]j - Pj)Y], i, j = h, l; I [not equal to] j

The factor [alpha]i represents the reservation price of the high fare or low fare good and we assume [alpha]h>[alpha]l.

Rearranging equation (2), we obtain the direct demand functions for high fare and low fare products:

In the producer side, we assume that there is one main airline company who provides one high fare good [X.sub.h] and possibly produces one low fare good [x.sub.l1] in its sub-company. Without any loss of generality, we assume that there exists one independent low fare airline company in the market who produces another low fare good, [x.sub.l2]. Therefore, the total quantity demanded of the low fare good is [X.sub.l] = [x.sub.l1] + [x.sub.l2].

The another assumption in the model is that the unit costs (per seat) of the high fare and low fare goods are constants as [c.sub.h] and [c.sub.l], [c.sub.h] >[c.sub.l] . However, unlike other industries the quantity demanded does not equal to the quantity supplied in the airline industry because load factors are usually less than one. Therefore, the total cost for either high fare or low fare good not only depends on the demand of the good but also depends on the output (11). To derive the total cost in the markets, we define the load factor [[lambda].sub.i] (i=h, l). Factor [[lambda].sub.i] is a function of the ratio of average occupied seats and capacity level in one particular

[[lambda].sub.i] = f(Xi/Ki) [less than or equal to] 1, [differential][lambda]i/[differential]Xi > 0, [lambda]i (1) = 1, and i = h, l

market (12), i.e.

where [K.sub.i] is the capacity level in i's good market.

2.1 Two-stage Game: the Main Airline Produces Both Types of Good

We frame this strategic decision as a two-stage game where the main airline also produces one low fare good. In the first stage of the game, the main airline and the low fare airlines play a Stackelberg game to set the quantities. In the second stage of the game, two low fare airline companies play a Cournot quantity setting game, given the quantity chosen by the high fare good in the first stage of the game. We start from the second stage in order to solve the game.

2.1.1 The Second Stage of the Game: Two Low Fare Airline Companies Compete in Quantity

In stage two, firm i's reaction function is derived from:

(4) [r.sub.li]([x.sub.lj]=argmax([P.sub.l][x.sub.li] - [c.sub.l][[X.sub.li]/[[lambda].sub.l]]) = [[[alpha].sub.l] - [[beta].sub.l]([x.sub.li] + [x.sub.lj]) - Y[X.sub.h]][x.sub.li] - [c.sub.l.sup.*][x.sub.li] i, j=1, 2; i [not equal to] j

where [c.sub.l.sup.*] is the relative cost in the low fare good market which is represented as [c.sub.l]/[[lambda].l]. This relative cost captures the feature that the total costs depend on the load factor and the capacity of the plane.

The first order condition for maximum profit for Equation (4) can be solved to yield:

(5) [x.sub.l1] = [x.sub.l2] = [x.sub.l] = 1/3 [[beta].sub.l] ([[theta].sub.l] - Y [X.sub.h])

where [[theta].sub.l] = ([alpha] - [c.sub.l.sup.*) and reflects the firm=s net absolute cost advantage. We consider later the importance of this element for the firm=s choices and market outcomes.

Hence, the total low fare output is:

(6) [X.sub.l] = [x.sub.l1] + [x.sub.l2] = 2/3[[beta].sub.l] ([[theta].sub.l] - y[X.sub.h])

Given this expression for [X.sub.l], we turn to the first stage of the game--the Stackelberg competition between high fare and low fare products

2.1.2 The First Stage of the Game: Main Airline Company and Two Low Fare Companies Compete in Quantity

Substituting the total low fare output function (6) back into (2), the indirect consumer demand functions can be re-expressed as:

(7) [P.sub.h] = [[alpha.sub.h] - 2y [[theta].sub.l]/3[[beta].sub.l] - [3[[beta].sub.h][[beta].sub.l] - 2[y.sup.2]/3[[beta].sub.l]] [X.sub.h]

(8) [P.sub.l] = [[alpha].sup.l] - 2[[theta].sub.l]/3 - [Y/3] [X.sub.h]

The main airline's joint profit maximization task is the selection of [X.sub.h] so as to maximize:

(9) [[pi].sub.h] = [P.sub.h] [X.sub.h] - [c.sub.h] [[X.sub.h]/[[lambda.sub.h]] + [P.sub.l][x.sub.l1] - [c.sub.l] [[X.sub.l1]/[[lambda].sub.l]] = ([P.sub.h] - [c.sub.h.sup.*])[X.sub.h] + ([P.sub.l] - [c.sub.l.sup.*])[x.sub.l1]

Once again, the parameters [[lambda].sub.h] and [c.sub.h.sup.*] represent the load factor and the relative costs in the high fare good market. Substituting (5), (7) and (8) into (9), differentiating and solving for [X.sub.h] we obtain the Stackelberg output of the high fare product in the two-stage game, [X.sub.h.sup.s2]:

(10) [x.sup.s2.sub.h] = [9[[beta].sub.l][[theta].sub.h] - 8y [[theta].sub.l]]/2(9[[beta].sub.h][[beta].sub.l] - 7[y.sup.2])

where [[theta].sub.h] = ([[alpha].sub.h] - [c.sub.h.sup.*]) is the net absolute cost advantage of high fare good production.

Substituting (10) into equation (5) we obtain the Stackelberg output of the low fare production in the two-stage game, [x.sub.l.sup.s2]:

(11) [X.sup.s2.sub.l] = [[theta].sub.l] / 3[[beta].sub.l] - [9[[beta].sub.l]y[[theta].sub.h] - 8 [y.sub.2][[theta].sub.l]/6(9[[beta].sub.h][[beta].sup.2.sub.l] - 7[[beta].sub.l][y.sup.2])

In this case the main airline aggregate profit is:

(12) [[pi].sup.s2.sub.h] = [([theta].sub.h] - 2y [[theta].sub.l]/3[beta].sub.l] - [[3[[beta].sub.h][[beta].sub.l] - 2[y.sup.2]]/3[[beta].sub.l]][X.sup.s2.sub.h]) [X.sup.s2.sub.h] + 1/9[[beta].sub.l]([[theta].sub.l] - y[x.sup.s2.sub.h]).sup.2]

2.2 One Stage Game: The Main Airline Produces Only High Fare Good

When the main airline does not pursue the spin off strategy it becomes a one-stage Stackelberg game. Retaining the assumptions from the previous section but adding the constraint that [x.sub.l1] = 0 so that [X.sub.l] = [x.sub.l2], the main airline company and low fare company now play a one-stage Stackelberg quantity-setting game.

In the one-stage game, the reaction function of the low fare firm is derived from:

[r.sub.l]([X.sub.h]) = argmax ([P.sub.l][X.sub.l] - [c.sub.l] [[X.sub.l]/[[lambda].sub.l]]) = ([alpha].sub.l] - [[beta].sub.l] [X.sub.l] - y[X.sub.h])[X.sub.l] - [c.sub.l] * [X.sub.l]

which yields:

(13) [X.sub.l] = 1/2[[beta].sub.l]([[theta].sub.l] - y[X.sub.h])

The objective of the high fare producer is to maximize:

(14) [[pi].sub.h] = [P.sub.h][X.sub.h] - [c.sub.h] [[x.sub.h]/[[lambda].sub.h]] = ([[alpha].sub.h] - [[beta].sub.h] [X.sub.h] - y[X.sub.l])[X.sub.h] - [c.sub.h] * [X.sub.h]

Substituting the low fare firm=s reaction function (13) into (14) we derive the main airline's single-stage Stackelberg output [X.sub.h.sup.s1] as:

(15) [X.sup.s1.sub.h] = [2[[beta].sub.l][[theta].h] - y[[theta].sub.l]]/[4[[beta].sub.h][[beta].sub.l] - 2[y.sup.2]]

Thus, substituting for [X.sub.h.sup.s1] into (13), the low fare firm=s output becomes:

(16) [X.sup.s1.sub.l] = [(4[[beta].sub.h][[beta].sub.l] - [y.sub.2])[[theta].sub.l] - 2[[beta].sub.l]y[[theta].sub.h]]/[8[[beta].sub.h][[beta].sup.2.sub.l] - 4[[beta].sub.l] [y.sup.2]]

Therefore, the main airline's Stackelberg profit in one stage game is,

(17) [[pi].sup.s1].sub.h] = ([[theta].sub.h] - y[[theta].sub.l]/2[[beta].sub.l] - [2[[beta].sub.h][[beta].sub.l] - [y.sup.2]/2[[beta].sub.l]] [X.sup.s1.sub.h])[X.sup.s1.sub.h]

3. COMPARISON ANALYSIS: TO PRODUCE LOW FARE GOOD OR NOT

Now, we can discuss and compare the strategic options for the main airline comany. Certainly, the airline company and social planner have diferent objectives in the business. The main airline company will pursue the strategy if its profit increases while social planner is looking for welfare improvement. Therefore, we conduct the following comparison analysis between two situations: produce low fare good or not from the views of profit and welfare respectively.

3.1 The Profit Comparison

Comparing the two-stage game profit [[pi].sub.h.sup.s2] with the one-stage game profit [[pi].sub.h.sup.s1] for the main airline, we find

[[pi].sup.s2.sub.h] > [[pi].sup.s1.sub.h] if [X.sup.s2.sub.h] > [X.sup.s1.sub.h]

or (13)

(18) y > [([[phi].sup.2] + 7[[beta].sub.h][[beta].sub.l]).sup.1/2] - [phi] where [phi] = [5/2][[beta].sub.l][[[theta].sub.h]/[[theta].sub.l]]

Proposition 1

The high fare airline will find it profitable to spin off a low fare alternative if the magnitude of y, the cross effect between the high fare and low fare goods is sufficiently large; that is, if:

y > [([[theta].sup.2] + 7[[beta].sub.h][[beta].sub.l]).sup.1/2] - [phi] where [phi] = [5/2][[beta].sub.l][[[theta].sub.h]/[[theta].sub.l]]

When the factor of cross price elasiticity is large, the high fare airline can take a larger share of the total market from its low fare rival by spinning off its own low fare airline. Assuming that the low fare spin-off produces airline seats at the same unit costs as the low fare rival, total profits for the high fare airline will increase.

Proposition 1 however, is subject to a corollary. Inequality (18) is more likely to hold when the ratio of [[theta].sub.h] /[[theta].sub.l] is relatively large; i.e. the ratio of the net absolute cost advantage of the high fare good to low fare good.

Corollary 1.

A main airline is more likely to spin off a low fare alternative the larger is the net absolute advantage of its high fare good relative to the net absolute advantage of low fare supply, i.e.

[[theta].sub.h]/[[theta].sub.l] > 6/5 [([[beta].sub.h]/[[beta].sub.l]).sup.1/2]

Proof:

Let

[rho] = [[beta].sub.h][[beta].sub.l]

then inequality (18) becomes

[([[phi].sup.2] + 7[rho]).sup.1/2] - [phi] < [[rho].sup.1/2] [??] [([[phi].sup.2] + 7[rho]).sup.1/2] < [[rho].sup.1/2] + [phi]

Squairing both side of above inequality, we have

3[[rho].sup.1/2] < [phi]

or

[[theta].sub.h]/[[theta].sub.l] > 6/5 [([[beta].sub.h]/[[beta].sub.l]).sup.1/2]

Q.E.D.

Stated another way, there is an incentive for the high fare airline to create a spin off when there exist a relatively small amount of empty seats on its high fare routes. When the load factors on high fare routes is not too small, it make sense to directly compete through a low fare spin off, since a small amount of high fare profit will be sacrificed to substitution. If there are already very low load factors on high fare routes than the spin-off strategy could actually reduce total profits for the airline because the profit gain from low fare routes may not cover the profit loss from high fare routes. This suggests that the spin off strategy may only work on certain routes.

This corollory represents a strategic decision rule for carrieres considering the low fare spin off strategy. In particular, this algorithm could be used in yield management systems. Yield management systems try to exploit opportunities for price discrimination by segmenting the various segmented demand curves present in an airline market. To our knowledge, these systems do not account for cross price elasticities with other carriers or total load factor in a market. Such enhancements may improve the future viability of spin-off discount carriers, by allowing them to Acherry pick@ potentially profitable markets. Such a development would be somewhat ironic since this is precisely the model that Southwest and the other discount start-ups have pursued to transform the market in the first place.

3. 2 The Welfare Comparison

Total societal welfare in this two good world can be represented as:

(19) W = U([X.sub.h], [X.sub.l] + w - [c.sub.h] * [X.sub.h] - [c.sub.l] * [X.sub.l]

where w represents a constant wage rate and is assumed constant (16). Totally differentiating the welfare function, yields:

(20) dW=([differential]U/[differential][X.sub.h] - [c.sub.h.sup.*])d[X.sub.h] + ([differential]U/[differential][X.sub.h] - [c.sub.h.sup.*]) d[X.sub.l] =([P.sub.h] - [c.sub.h.sup.*])d[X.sub.h] + ([P.sub.l] - [c.sub.l.sup.*])d[X.sub.l]

Suppose we start from a situation in which an airline does not spin off a low fare alternative and produces only its high fare good. The welfare change for the additional low fare is then:

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]

Since [P.sub.h] - [c.sub.h.sup.*] >0 and [P.sub.l] - [c.sub.l.sup.*] > 0, the sign of [DELTA]W is determined by d[X.sub.h] and d[X.sub.l]. As proved in the Appendix, subject to certain conditions, we have [X.sub.h.sup.s2] > [X.sub.h.sup.s1] and 2 [X.sub.l.sup.s2] > [X.sub.l.sup.s1]. Therefore, we have the following proposition (17).

Proposition 2

There will be both profit and welfare improvement from the spin-off strategy when the factor of cross price elasticity between two goods is large enough, i.e.

y > max {[([[phi].sup.2] + 7[[beta].sub.h][[beta].sub.l]).sup.1/2] - [phi], [([[phi].sup.2] - [304/1444][[[beta].sub.h][[beta].sub.l]).sup.1/2] + [phi]} where [phi] = [21/38][[beta].sub.l][[[theta].sub.h]/[[theta].sub.l]]

Proposition 2 shows that both profit and welfare can increase by the strategy of spin off if the factor of cross price elasticity is large enough. There will always be an increase in consumer surplus from the introduction of another low fare airline, but in some circumstances the consumer gain could be smaller than then the loss in producer surplus from pursing this strategy. If the factor of cross price elasticity is relatively large, there will be a large consumer surplus increase in low fare good market and this consumer gain is greater than the profit loss in high fare good market. More importantly, under the same condition the total profit of main airline counted from both its high fare business and low fare business is larger than the situation the airle only operates high fare routes. In other words, to the extent that these spin offs acclerate airline bankruptcies, total welfare can fall.

4. CONCLUSIONS

Our results suggest that any airline considering competition with a low cost carrier should closely examine the cross price elasticity of demand and the load factors on the high fare routes. To the extent that traffic is falling for exogenous or endogenous reasons, or cross elasticity are low, or the current high fare load factor is already low the strategy=s likelihood for success decreases. We believe that for many major and flag bearer airlines such as Air Canada, which at least one of these factors is in place and the likelihood of success of the spin off strategy seems low. We intend to estimate our models parameters to confirm this hypothesis.

APPENDIX

1. Proof of Proposition 1

Let

[X.sup.s2.sub.h] = [9[[beta].sub.l][[theta].sub.h] - 8y[[theta].sub.l]]/2(9[[beta].sub.h][[beta].sub.l] - 7[y.sup.2]) < [X.sup.s1.sub.h] = [2[[beta].sub.l][[theta].sub.h] - y[[theta].sub.l]]/[4[[beta].sub.h][[beta].sub.l] - 2[y.sup.2]]

or

(A1) 2[y.sup.2][[theta].sub.l] + 10[[beta].sub.l][[theta].sub.h]y - 14[[beta].sub.h][[beta].sub.l][[theta].sub.l] < 0

Solving (A1) for y,

y > [[(100[[beta].sup.2.sub.l][[theta].sub.h] + 112[[beta].sub.h][[beta].sub.l][[theta].sup.2.sub.l]).sup.1/2] - 10[[beta].sub.l][[theta].sub.h]]/4[[theta].sub.l] = [([25/4][[beta].sup.2.sub.l][[[theta].sup.2.sub.h]/[[theta].sup.2.sub.l]] + 7[[beta].sub.h][[beta].sub.l]).sup.1/2] - [5/2][[beta].sub.l][[[theta].sub.h]/[[theta].sub.l]]

In order to ensure the convexity of utility function, the following condition is kept.

[y.sup.2] < [[beta].sub.l][[beta].sub.h] or y < [([[beta].sub.l][[beta].sub.h]).sup.1/2]

2. The Social Welfare Function

W = U([X.sub.h], [X.sub.l], [X.sub.0]) + Y - [P.sub.h][X.sub.h] - [P.sub.l][X.sub.l] - [P.sub.0][X.sub.0]

Given consumer utility functions U ([X.sub.h] , [X.sub.l] , [X.sub.0]) with [X.sub.0] a numeraire good, society=s

aggregate welfare function can be written as:

(A2)

W = U([X.sub.h], [X.sub.l]) + Y - [P.sub.h][X.sub.h] - [P.sub.l][X.sub.l]

where Y represents money income and comprises the sum of profits, [pi] and wages, w. We assume the total wage bill is constant. Then, normalizing and setting the price of the numeraire good to unity:

(A3)

The total profits from both high fare good and low fare good can be written as:

(A4) [pi] = [P.sub.h] [X.sub.h] - [c.sub.h] * [X.sub.h] + [P.sub.l][X.sub.l] - [c.sub.l] * [X.sub.l]

and, substituting (w + [pi]) for Y, the total welfare function

becomes:

(A5) W = U([X.sub.h], [X.sub.l]) + w - [c.sub.h] * [X.sub.h] - [c.sub.l] * [X.sub.l]

3. Proof of Proposition 2

From (11) and (16), we know d[X.sub.l] = 2[X.sub.l.sup.s2] - [X.sub.l.sup.s1], i.e.

(A6) d[X.sub.l] = 2[[theta].sub.l]/3[[beta].sub.l] - [9[[beta].sub.l]y[[theta].sub.h] - 8[y.sup.2][[theta].sub.l]]/3(9[[beta].sub.h][[beta.sup.2.sub.l] - 7[[beta].sub.l][y.sup.2]) - [(4[[beta].sub.h][[beta].sup.2.sub.l] - [[beta].sub.l][y.sup.2])[[theta].sub.l] - 2[[beta].sub.l]y[[theta].sub.h]]/[8[[beta].sub.h][[beta].sup.2.sub.l] - 4[[beta].sub.l][y.sup.2]]

Let d[X.sub.l] >0 in (A6),

(A7) 2[[theta].sub.l]/3[[beta].sub.l] - [9[[beta].sub.l]y[[theta].sub.h] - 8[y.sup.2][[theta].sub.l]]/3(9[[beta].sub.h][[beta].sup.2.sub.l] - 7[[beta].sub.l][y.sup.2]) - [(4[[beta].sub.h][[beta].sup.2.sub.l] - [[beta].sub.l][y.sup.2])[[theta].sub.l] - 2[[beta].sub.l]y[[theta].sub.h]]/[8[[beta].sub.h][[beta].sup.2.sub.l] - 4[[beta].sub.l][y.sup.2]] > 0

Since

3(9[[beta].sub.h][[beta].sup.2.sub.l] - 7[[beta].sub.l][y.sup.2]) > 8[[beta].sub.h][[beta].sup.2.sub.l] - 4[[beta].sub.l][y.sup.2]

(A7) holds if

(A8) 2[[theta].sub.l]/3[[beta].sub.l] - [9[[beta].sub.l]y[[theta].sub.h] - 8[y.sup.2][[theta].sub.l]]/[8[[beta].sub.h][[beta].sup.2.sub.l] - 4[[beta].sub.l][y.sup.2]] - [(4[[beta].sub.h][[beta].sup.2.sub.l] - [[beta].sub.l][y.sup.2])[[theta].sub.l] - 2[[beta].sub.l]y[[theta].sub.h]]/[8[[beta].sub.h][[beta].sup.2.sub.l] - 4[[beta].sub.l][y.sup.2]] > 0

(A8) is hold based on the following condition:

(A9) 19[[theta].sub.l][y.sup.2] - 21[[beta].sub.l][[theta].sub.h]y + 4[[beta].sub.h][[beta].sub.l] > 0

Transforming (A9), we have two ceiling for y,

y > [phi] + [([[phi].sup.2] - [304/1444][[beta].sub.h] [[beta].sub.l]).sup.1/2], or y < [phi] - [([[phi].sup.2] - [304/1444] [[beta].sub.h][[beta].sub.l]).sup.1/2], where [phi] = [21/38][[beta].sub.l] [[[theta].sub.h]/[[theta].sub.l]]

Combining the condition for Proposition 1, we know that dW>0 if

y > max{[([[phi].sup.2] + 7[[beta].sub.h][[beta].sub.l]).sup.1/2] - [phi], [([[phi].sup.2] - [304/1444][[beta].sub.h][[beta].sub.l]).sup.1/2] + [phi]}

End Notes

(1.) The estimated savings--due to actual, adjacent, and potential competition from Southwest--were $12.9 billion. Southwest's low fares were directly responsible for $3.4 billion of these savings to passengers. The remaining $9.5 billion represents the effect that actual, adjacent, and potential competition from Southwest had on other carriers' fares. These savings amount to 20 per cent of the airline industry=s 1998 domestic scheduled passenger revenue and slightly more than half the fare reductions attributed to airline deregulation.@ (Morrison, 2001).

(2.) The precise measurement of these broad parameters varies throughout the literature but for our purposes, we will consider yield to revenue per unit of output so that it can be easily compared to cost per unit of output. It is well known that output (supply) is not equal to traffic (demand) for airlines, ie the load factor is often less than one.

(3.) The Department of Transport reports that Southwest airlines have the fewest customer complaints among passengers in each of the last 10 years.

(4.) US Airways, United and American represent 45% of the US airline industry.

(5.) Of course, part of the strategy is to also request government assistance. Significant bailout packages to stabilize the industry and protect the public good have been supported in principle by both the US and Canadian governments. Not surprisingly, the current profitable airlines are not supportive of such proposals. A it=s a classic example of helping a failed organization@ B Clive Beddoe, CEO West Jet as quoted in the Financial Post, March 31st, 2003.

(6.) This is not strictly a North American phenomenon. There are many examples in Europe including BA Regional and Lufthansa Express launched in 1992 and throughout the world such as Freedom Air in New Zealand and Japan Air Charter. The latter two, in contrast to the North American experience, have been relatively profitable and both remain in operation.

(7.) This point was made emphatically in an April 17th, 2003 Globe and Mail editorial/opinion by Brian Campbell, A drop the multiple branding. Creating airlines within airlines, such as Air Canada's Tango, will not be successful as a strategy for addressing low-fare competitors. The Air Canada brand is enormously powerful and should be leveraged everywhere. It will work for 70 to 80 per cent of the market between the two price extremes.@

(8.) As an example of these risks, consider Tango and Zip launched by Air Canada in 2001. It was clear after flying on both services that a real effort to incorporate the no-frill culture was evident in Zip (all that was missing was the vending machines dispensing food) but not on Tango which still had many of the same services and style of Air Canada.

(9.) In reference to the development of Tango and Zip, A I think Robert Milton (CEO of Air Canada) is a genius. He has pursued a brilliant and innovative strategy.@ B Stanley Hart, Globe and Mail, p. B4, April 5th, 2003.

(10.) Getting this strategy right is important for three reasons beyond viability. First, bankruptcy restructuring should be conducted efficiently. Second, potential buyers or investors in the bankrupt or near bankrupt airlines, need to evaluate whether these spin offs are capable of realizing profits as stand alone entities. Finally, any public resources committed to helping these airlines must be allocated to receive the highest rate of public return.

(11.) The total cost of does not equal [c.sub.h] or [c.sub.l] multiplied to the total output because the empty seats will cost less than occupied seats. For example, we need not serve food and beverage for the empty seats.

(12.) In order to simplify the model, we use the average occupied seats in the market to construct the load factor [[lambda].sub.i]. Therefore, [[lambda].sub.i] is an exogenous variable in the model.

(13.) See Appendix for the proof.

(14.) The anecdotal evidence presented earlier casts some doubt on this assumption.

(15.) We have the condition of [y.sup.2] < [[beta].sub.h][[beta].sub.l], to ensure convexity of the utility function

(16.) See Appendix for the proof.

(17.) See Appendix for the proof.

REFERENCES

Holloway, Stephen. Straight and Level: Practical Airline Economics. Great Yarmouth: Galliard (Printers) Ltd., 1997.

Morrison, Steven, "Actual, Adjacent, and Potential Competition: Estimating the Full Effect of Southwest Airlines", Journal of Transport Economics and Policy, 35(2) (2001): 239-56.

O'Connor, William, An Introduction to Airline Economics. 6th ed. Westport, CT: Praeger Publishers, 2001.

Richards, Krista, "The Effect of Southwest Airlines on U.S. Airplane Markets", Research in Transportation Economics. 4 (1996): 33-47.

Steven Berry, Michael Carnall, and Pablo Spiller, @ Airline Hubs: Costs, Markups and the Implications of Customer Heterogeneity", National Bureau of Economic Research Working Paper, 5561 (1996): 20.

Tae Hoon Oum, A Key Aspects of Global Strategic Alliances and the Impacts on the Future of Air Canada and other Canadian Air Carriers", Research conducted for the Canada Transportation Act Review, (2001).

Tae Hoon Oum, Jong-Hun Park, and Anming Zhang, Globalization and Strategic Alliances: The Case of the Airline Industry, Netherlands: Pergamon, 2000.

Williams, George, The Airline Industry and the Impact of Deregulation, Cambridge: University Press, 1993.

Dr. Ying Kong earned his Ph.D. at Carleton University in 2000. Currently he is an assistant professor at School of Business and Economics, University College of the Cariboo, Canada.

Dr. Andre Le Dressay earned his Ph.D. at Simon Fraser University. Currently he is the director of Fiscal Realities Associates, Canada.

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