Theoretical models are formulated for airline firm operations that revolve around alternative formulations of managerial goals which these firms are persuing in practice. Consideration is given to the different objective functions which the companies are following in lieu of profit maximization

Kneafsey, J. T.

English

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Objectives of the Airline Firm: Theory 
I. Introduction: Models of the Firm 
James T. Kneafsey 
Massachusetts Institute 
of Technology 
Friday, July 14, 1972 
Most analyses of dynamic pricing strategies in the economics 
literature have adhered to the assumption that business firms seek 
to maximize profits. Newer models of the behavior of large corpora-
tions have recently been developed in which a variety of assumptions 
about business motivation have been inserted into traditional static 
frameworks, steady-state growth models of the firm, and non-maximizing 
"behavioral" analyses. These new models have paid increasing attention 
to the nature and determinants of the forces governing the size and 
growth of the companies of which they are composed. In particular, 
the theoretical models of the growth of the firm are rapidly becoming 
more rigorous, comprehensive, and widely accepted. 
Since firms in the trunk airline industry compete in money and 
capital markets with numerous other firms in both the regulated and 
unregulated sectors of the economy, these models of firm behavior 
can be applied directly to the airline industry. The subject under 
discussion will revolve around alternative formulations of managerial 
goals whichairl ine firms may be pursuing in practice. The focus will 
be on the consideration of different objective functions which the 
companies may be following in lieu of profit maximization. Since these 
models reflect the behavior of any single firm in any industry, the 
analysis is one of partial equilibrium which assumes the activities of 
, 
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all other competitors as given. l 
This paper has two general purposes. It is intended mainly to 
provide a frame of reference from which alternative hypotheses can 
be stated concerning the objectives which managers and executives 
in the airline industry may be pursuing. It also incorporates as 
comprehensive a list as possible of alternative objective functions 
and demonstrates graphically that each separate objective may result 
in its own unique price (fare) and output (volume) combination when 
equilibrium occurs. 
II. Some Simplified Specifications of Alternative Objective Functions 
Using the revered goal (objective) of profit maximization as a 
base, we propose to analyze the following alternative objective 
functions: 
A. Short-run profit maximization 
B. Revenue maximization 
c. Sales maximization (break-even) 
D. Volume maximization 
lThfS restriction is severe with respect to the scope of economic 
questions, both analytical and practical, that can be answered. 
Economic analysis also seeks to investigate important subjects 
which concern systems of many firms, or of all firms, which require 
consideration not only of how all firms individually behave, but 
also of how their individual activities interact with and constrain 
each other in markets, broad sectors and the whole economy. 
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E. Cost minimization 
F. Constrained sales maximization 
1. Minimum value profits 
2. Ascending buffer 
3. Descending buffer 
G. "Satisficing" 
H. Other specifications (non-graphical) 
1. Utility maximization 
2. Growth maximization 
3. Stockholder equity maximization 
4. Security maximization 
5. Market share equalization 
Each case will be examined separately to determine the resulting 
price-output combination which optimizes each alternative objective 
function. By nature these models are simplistic yet the underlying 
importance of the basic demand-supply relationships is reflected in 
the sharply different results of each model. In essence the shapes 
of the revenue and cost functions (or demand and supply) determines 
the optimal price-output combination for each alternative objective. 
A. Short-run Profit Maximization 
Revenues are derived from the demand function and are depicted 
in Figure 1 (top) as a concave function (to the origin), that is, 
RR = P x Z where P is fare and Z represents output (or volume of 
passengers). Assuming that fares can be changed and that the law of 
demand applies (dZ /~P < 0), R reaches a maximum at point B. 
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However. to generate profits. a knowledge of costs is necessary. 
If costs are a function of volume. they can be depicted typically as 
CC in Figure 1 (top). Profits are simply the algebraic difference be-
tween RR and CC at each alternative level of Z, and are maximized 
when RR exceeds CC by the greatest amount (point A in Figure 1). the 
result being a profit curve TI (Figure 1. middle). The equating of 
marginal costs (MC) and marginal revenue (MR) (Figure 1. bottom) for 
those of you who prefer to think in unit terms will occur exactly 
at point A. 
B. Revenue Maximization 
With the shape of the present RR curve. revenues are maximized 
at its peak (point B in Figure 1, top). This result also obtains 
where MR = 0 because additional Z can only occur with a decline in 
revenues as a result of the law of demand in operation. MR is simply 
the slope of the RR curve (dRR/ AZ). 
C. Sales Maximization (break-even) 
There are different variations of the sales maximization hypothesis. 
In this case we are referring simply to carrying as many passengers (Z) 
out to the break-even point C. For reasons of market penetration, the 
airline may neither be interested in the short-run in profits nor in 
revenues. but rather it is interested in trading off less profits or less 
revenues for more customers. 2 
2The typical distinction between cost in the economic sense and in the 
accounting sense should be made. In economic terms. CC includes as a 
component a normal rate of return such that TI really refers to "excess" 
profit. In the account sense. CC is the conventional income statement 
figure which excludes profit. 
/ /' 
/ 
--
1 
0J 
// ---
I / T' Ro r- I I 
1/ <:: 
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, 
Figure 1: Total Dollars ($), Profits (~), and Dollars 
per Unit ($jZ) Plotted Against Output (zl 
( 
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D. Volume Maximization 
An extension of the sales maximization hypothesis is that an 
airline firm may wish to carry as many passengers as possible, even 
if it results in a short-term loss. The result is in effect an objective 
of maximizing all available capacity (point 0 in Figure 1, top). Note 
that a large bias would be incurred with the pursuit of this objective 
function with the present revenue and cost relationships. 
E. Cost Minimization 
Sometimes companies become extremely cost conscious and pursue 
the goal of cost minimization (point E in Figure 2). This output 
level occurs at the bottom of the average cost curve (AC) where MC = 
AC. It is an objective completely independent of demand influences, 
unlike the goals discussed above. A danger which companies occasionally 
and regrettably experience is that they may minimize themselves to death 
if revenue considerations are ignored. If the demand curve (AR in unit 
terms or RR/Z)lies far below where it does in Figure 2, then cost 
minimization as a corporate objective still would not help. As it 
turns out in the present case, total profits are depicted by the 
hatched area in Figure 2. 
. Figure 2: 
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Dollars per Unit ($/Z) 
Plotted Against Output (Z) 
• 
Me.. 
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F. Constrained Sales Maximization 
1. Minimum Value Profits 
This hypothesis has been advanced by a number of economists with 
W. J. Baumo1 in the Vanguard. In the most complete statement of his 
proposition, Baumo1 argued that firms with market power tend to 
maximize sales subject only to the condition that profits not fall 
below some specified minimum va1ue. 1 In Figure 3, profits are 
maximized at A. However, if management feels that a certain level of 
profits is satisfactory or even necessary to maintain (OM in Figure 3, 
bottom) irrespective of volume (Z), then the company's goal is over-
fulfilled at volume OA. It can increase volume to O(F1) while earning 
at least OM in profits, enjoying higher "sales" than it would under 
a short run profit maximization policy. If the company's managers 
insist on earning profits of ON before seeking to satisfy other objectives 
such as sales maximization, they will not be in a position to increase 
revenues beyond the short-run profit maximizing level since the profit 
objective lies out of reach. The most important implication of this 
analysis is that if firms in the airline industry in fact strive to 
increase revenues for its own sake and if they require less profit to 
meet capital needs (e.g., OM in Figure 3), then they can charge lower 
fares and offer more volume than they would under the goal of profit 
maximization. Two variations of this objective are the ascending and 
descending buffer objectives. 
1See William J. Baumo1, Business Behavior, Value, and Growth, rev. ed., 
New York: Harcourt, Brace and World, 1967, pp. 45-82 and 86-104. 
N---' 
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1 
I 
. __ -+~ __ ~I~ ___________ i_~_;r!~-________ ___ 
'J.; ~ ....... 
1--
O\'-· ----'-------t? -_._----/---::....._--
'A (fl 
Figure 3: Contrained Sales Maximization 
/ 
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2. Ascending Buffer 
In Figure 3, OM represents a "buffer" of profits which the 
firm desires to earn. These profits may be used for unexpected 
financing purposes, for dividend declarations, or for retained 
earnings. As long as OM is earned, the company will sacrifice additional 
profits for more sales. In Figure 4, KK represents a buffer stock of 
profits which increases with volume 2. With more and more volume pre-
sumably the firm should be in a stronger position to increase dividends 
or to finance additional expenditures. An allowance for this growth is 
reflected in the rising slope of KK. In this case the company will 
select volume (F2) in Figure 4, where sales are maximized subject to the 
buffer (KK) constraint. 
3. Descending Buffer 
Alternatively firms may be willing to sacrifice substantial short 
run profits in order to generate volume which would result in a buffer 
stock LL that varies negatively with volume. If volume during a given 
period is decreased sharply. say as a result of a strike, the company 
may wish to have a larger profit buffer at low ranges of Z. As volume 
increases though, the tradeoff with profits becomes apparent and the 
company wouid opt for output (F3) in Figure 4. 
G. "Satisficing" 
In the early 1960's, several economists in the Graduate School 
of Administration at the then Carnegie Institute of Technology developed 
the "behavioral" theory of the firm. At the heart of this theory lies 
the concept of "satisfi cing", usually attributed to the work of Herb Simon. 
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Essentially satisficing refers to the fact that firms may not be 
maximizing at all but rather may be pursuing a number of goals 
simultaneously resulting in accepting a "satisfactory" level of 
profits. Graphically, this means that the firm can select any volume 
in Figure 4 as long as some satisfactory level of profits is attained. 
In the case of pursuing any profit at all, the range would be QC 
within which the firm would be "satisfied". 
H. Other Specifications (non-graphical) 
Numerous other objectives could be pursued by firms in practice 
either individually or jointly. These goals might include the 
maximization of a firm's utility function, of its rate of growth of 
output, or of its stockholders' equity. Since ownership and manage-
ment are separate functions of airlines and other large companies, 
an important objective to analyze might be the maximization of the 
management's own security and stability. Also, the companies might 
be satisfied with maintaining or increasing market shares as an 
objective independent of any other one. 
The goals in this section cannot be demonstrated graphically as 
we have done with the other alternatives. For those objectives which 
we have discussed, a summary version of each alternative volume 
appears in Figure 5. 
III. Concl usion 
No one has yet succeeded in demonstrating conclusively whether 
or not airlines or other business firms behave in the ways and for 
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K ---'-v-o/~- -.-_. ~~- -
01'----:---·-··-·····--- .... ~ 
Figure 4: Ascending and Descending Buffer 
Objectives; and "Satisficing" 
" , 
/ 
/ 
./ r 
./ 
I 
i 
I 
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J.-----.-!Q-,- --~l tt:i--~--t-t--~-
(fl) \f2-)(f3) 
--- n_ G-' ;; 
Figure 5: Objectives of the Airline Firm--
Summary (See pp. 2-3) 
A - Short-run profit maximization 
B - Revenue maximization 
C - Sales maximization (break-even) 
D - Volume maximization 
E - Cost minimization 
Fl - Minimum value profits 
F2 - Ascendi ng bu ffer 
F3 - Descending buffer 
G - "Satisficing" (pJ../ & 
/1 
/\ 
/ 
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the reasons postulated in the above models of selecting alternative 
objective functions. One obstacle to enlightenment is that the be-
havioral differences between long run profit maximization and various 
short run alternative goals are so subtle that econometric tests 
with existing data are not sufficiently powerful to discriminate 
among the contending hypotheses. Since it is clear that airlines do 
pursue one or more of these objectives in practice, the present state 
of knowledge certainly must be extended through more sophisticated 
econometric research and by more detailed case studies than any here-
tofore attempted. 


Objectives of the Airline Firm: Theory

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