Anyone who has traveled via commercial airline, even on an infrequent
basis, knows there is a bewildering plethora of fares for the same route.
Besides the standard first-class and coach fares, there are discount fares
for round-trip travel and for travelers who book two or more weeks in
advance, leave during the week, stay over Saturday night, or fly standby.
The fare structure is daunting not only for travelers but also for the
airlines. In determining the standard coach fare on a particular route, the
airline has to consider (1) the cost of the flight (including fuel, labor, and
administrative costs), (2) the historical pattern of business and leisure use
on the route, (3) overall economic conditions (which affect travel
demand), and (4) the prices charged by competing airlines. Together the
airlines mount some 31,000 domestic flights each day, and they
repeatedly alter prices on their computerized reservation systems as
conditions change.
Among airlines, the name of the game is yield management: how to price
seat by seat to generate the greatest possible profit. For instance, airlines
typically sell higher-priced tickets to business travelers who cannot take
advantage of supersaver and other discount fares. At the same time, they
sell other seats on the same flight at sharply lower prices to attract price-
sensitive vacation travelers.
The question here is: How can demand analysis help the airlines win the
game of yield management?
up until now we have studied the dependence of demand on a single
factor: price. We begin this chapter by considering the multiple
determinants of demand. Next, we look more closely at the
responsiveness of demand to these factors, a concept captured in the basic
definition of elasticity. In the remaining sections, we present a richer
formulation of demand and show how it can be used to guide managers in
their goal of maximizing profits. Toward this end, we will refine our
optimization techniques to account for more complicated demand
conditions—those that include the possibilities of market segmentation
and price discrimination.
DETERMINANTS OF DEMAND
The Demand Function
To illustrate the basic quantitative aspects of demand, let’s start with a
concrete example: the demand for air travel.2 Put yourself in the position
of a manager for a leading regional airline. One of your specific
responsibilities is to analyze the state of travel demand for a nonstop
route between Houston, Texas, and a rapidly growing city in Florida.
Your airline flies one daily departure from each city to the other (two
flights in all) and faces a single competitor that offers two daily flights
from each city. Your task is complicated by the fact that the number of
travelers on your airline (and therefore the revenue your company earns)
has fluctuated considerably in the past three years. Reviewing this past
experience, you realize the main determinants of your airline’s traffic are
your own price and the price of your competitor. In addition, traffic
between the two cities was brisk during years in which the Texas and
Florida economies enjoyed rapid expansion. But, during the slowdown of
2008, air travel fell between the two cities.
Your immediate goal is to analyze demand for coach-class travel between
the cities. (The small aircraft used on this route does not accommodate
first class seating.) You begin by writing down the following demand
function: Q = f(P, P°, Y2.) (3.1)
This expression reads, “The number of your airline’s coach seats sold per
flight (Q) depends on (is a function of) your airline’s coach fare (P), your
competitor’s fare (P0), and income in the region (Y).” In short, the
demand function shows, in equation form, the relationship between the
quantity sold of a good or service and one or more variables.
The demand function is useful shorthand, but does not indicate the exact
quantitative relationship between Q and P, P_, and Y. For this we need to
write the demand function in a particular form. Suppose the economic
forecasting unit of your airline has supplied you with the following
equation, which best describes demand:
Q =25 + 3Y + P° + 2P. (3.2)
Equation 3.2 predicts sales quantity once one has specified values of the
explanatory variables appearing on the right-hand side. What does the
equation say about the present state of demand? Currently your airline
and your competitor are charging the same one-way fare, $240. The
current level of income in the region is 105.4 Putting these values into
Equation 3.2, we find that
Q = 25 + 3(105) + 1(240)+ 2(240)
= 100 seats
A comparison of this prediction with your airline’s recent experience
shows this equation to be quite accurate. In the past three months, the
average number of coach seats sold per flight (week by week)
consistently fell in the 90- to 105-seat range. Since 180 coach seats are
available on the flight, the airline’s load factor is 100/180 =55.5 percent.
The demand equation can be used to test the effect of changes in any of
the explanatory variables. From Equation 3.2, we see that
1. For each point increase in the income index, 3 additional seats will be
sold.
2. For each $10 increase in the airline’s fare, 20 fewer seats will be sold.
3. For each $10 increase in the competitor’s fare, 10 additional seats will
be sold.
The Demand Curve and Shifting Demand
Suppose that, in the immediate future, regional income is expected to
remain at 105 and the competitor’s fare will stay at $240. However, your
airline’s fare is not set in stone, and you naturally are interested in testing
the effect of different possible coach prices. Substituting the values of Y
and P0 into Equation 3.2’s demand function, we find that
Q = 25 + 3(105) + 1(240) – 2P,
=580 – 2P (3.4)
Like the basic demand equation facing the microchip producer in Chapter
2, Equation 3.4 relates the quantity of the good or service sold to its price.
Here, however, it is important to remember that, in the background, all
other factors affecting demand are held constant (at the values Y =105
and P0 = 240). Of course, it is a simple matter to graph this demand
equation as a demand curve. (Do this yourself as practice.) As usual, the
