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Outline
•Airline ticket pricing
•The demand function
•Determinants of demand
•Elasticity of demand
•Price elasticity, revenue, and marginal revenue
Airline ticket pricing
Consider United Airlines Flight
815 from Chicago to LA on October
31, 19971
•There were 27 different one-way fares, ranging from
$1,248 for a first class ticket purchased the day of the
flight to $87 for an advance purchase coach ticket.
•Some travelers cashed in frequent flier miles.
•Some qualified for senior citizen discounts.
•Some passengers traveled on restricted tickets that
required Saturday stayovers.
1”So, How much did you pay for your ticket,” New York Times, April 12,
1998
Yield management
“Yield management” means
pricing seats to maximize profits.
Our task in this chapter is
demonstrate how demand analysis
can be useful useful in establishing
a profit maximizing fare
structure—albeit one that is
bewildering to travelers
Assumptions
1. You are a manager for a regional airline offering
non-stop service between Houston, TX and
Orlando, FL.
2. Your airline makes one departure from each city
per day (2 flights total).
3. One rival airline offers non-stop service on this
route.
4. We ignore first class service and focus on the
demand for coach-class travel.
The demand function
Q = f(P, PO, Y)
[3.1]
[3.1] can be read as follows: The number of your
airline’s coach seats sold per flight (Q) is a
function of the your airline’s coach fare (P), its
rival’s fare (PO), and income in the region (Y)
Your forecasting unit has estimated
the following demand function:
Q = 25 + 3Y + PO – 2P
[3.2]
Effect of changes in the explanatory variables
Q is the dependent
variable; P, PO, and Y
are the independent or
explanatory variables.
1. For each one point increase in the income index
(Y), 3 additional seats will be sold, ceteris paribus.
2. For each $10 increase in the airline’s fare, 20 fewer
seats will be sold, ceteris paribus.
3. For each $10 increase in the competitor’s fare, 10
additional seats will be sold, ceteris paribus.
The demand curve
Definition: Curve indicating the
quantities demanded of a good or
service (such as air service) at
various prices (fares, etc.), ceteris
paribus.
Example: Let Y = 105 and PO = $240. Our demand
function is given by:
Q = 25 + 3(105) + 1(240) –2P = 580 – 2P [3.4]
Our inverse demand function is given by:
P = 290 – Q/2
[3.4a]
Ceteris paribus
Remember that as we
move along the demand
curve we hold “all other
things” constant. In our
case this means Y and PO
Price
290
240
P = 290 - Q/2
219
100
142
580
622
Quantity of Units Sold
Shifts of the demand curve
Price
$311
290
P = 311 - Q/2
240
What would happen if,
ceteris paribus, Y
increased to 119? Work it
out and you will discover
the new inverse demand
function is given by
P = 311 – Q/2
P = 290 - Q/2
100
142
580
622
Quantity of Units Sold
Normal and inferior goods
•A product (or service) is said to be a
normal good if an increase in income
raises its sales, ceteris paribus—that is, the
coefficient of Y is positive.
•Air travel, cellular service, and luxury
automobiles are examples of normal goods.
•Conversely, an inferior good has a
negative income coefficient.
•Macaroni and hot dogs are examples of
inferior goods.
Substitutes and complements
•If an increase in the price of good Y causes an increase
in the demand for good X (shift to the right), then X and
Y are substitutes.
•Examples of substitutes include: car and air travel;
chicken and pork; doctors and midwives.
•If an increase in the price of good Y causes an decrease
in the demand for good X (shift to the left ), then X and Y
are complements.
• Examples: PCs and digital cameras; tents and sleeping
bags; TVs and DVD players; shotguns-camo.
Other influences on demand
1. Population growth—e.g., as the population of
Houston and Orlando expands, the demand curve
for air service increase.
2. Demographic changes—e.g., aging population
increases demand for Celebrex© or other arthritis
medications; decrease in the share of the population
18-45 reduces the demand for beer.
3. Tastes & preferences—e.g, in reaction to evidence
of the health benefits of moderate wine
consumption.
Elasticity
Issue: How responsive is the
demand for air service to
changes in fares, ceteris
paribus. The concept of
price elasticity of demand is
useful here.
Price elasticity of demand
Let price elasticity of demand (EP) be given by:
% change in Q
EP =
% change in P
Q / Q0 (Q1  Q0) / Q0


P / P 0
( P1  P 0) / P 0
[3.1]
Price
Example
A
240
235
0
B
100
P = 290 – Q/2
110
Output
Question: What is EP in the range of demand curve
between fares of $240 to $235? To find out:
(110100) /100
10%
p 

 4.8
( 235 240) / 240
 2.1%
E
Meaning, a 1% increase in fares will result in a 4.8%
decrease in passengers per flight (and vice-versa).
Point elasticity
In our previous example we
computed the elasticity for a certain
segment of the demand curve
(point A to B). For purposes of
marginal analysis, we are interested
in point elasticity—meaning,
elasticity when the change in price
in infinitesimally small.
Formula for point elasticity
dQ / Q  dQ  P 
EP 

 
dP / P  dP  Q 
[3.11]
Here we are calculating
the responsiveness of
sales to a change in
price (fares) at a point
on the demand curve—
that is, a defined pricequantity point .
Arc elasticity
To compute arc elasticity, or “average” elasticity
between two price-quantity points on the demand curve:
Q
Q / Q
(Q 0  Q1) / 2
EP 

P
P / P
( P 0  P1) / 2
Samuelson and Marks note the advantage of arc
elasticity—that is, it matters not what the initial price is
(say, $240 or $235), our calculation of EP does not change.
Perfectly inelastic demand
Price
$100
Buyers are
absolutely nonresponsive to a
change in price
90
80
70
60
50
EP = 0
40
30
20
10
0
50
100
150
200
250
Quantity
In this case, if the
price rises a
penny above $5,
quantitydemanded falls to
zero.
Perfectly elastic demand
Price
$10
9
8
7
6
EP = - infinity
5
4
3
2
1
0
50
100
150
200
(b) Perfectly Elastic Demand
250
Quantity
Income elasticity
Issue: Is demand for a good or service
sensitive to a change in consumer income,
ceteris paribus?
Income elasticity of demand (EY) is given by:
%Q Q / Q
EY 

%Y
Y / Y
Where Y is consumer income
Cyclical sales?
•If EY > 1, then sales are cyclical—that is, sensitive to
economic (business cycle) fluctuations.
•Autos, furniture, and major appliances are examples
of cyclical industries.
•If EY < 0, then sales are counter-cyclical. An overall
decrease in consumer income will result in an
increase in sales for these products.
•Examples: Pawnbroker services, macaroni, bus travel
Cross price elasticity of demand
1. How sensitive is the demand for rental
cars to airline fares?
2. How does the demand for apples respond
to a change in the price of oranges?
3. Will a strong dollar hurt tourism in Florida?
Cross price elasticity gives us a
measure of the responsiveness of
demand to the price of complements
or substitutes
Formula for cross price elasticity
Cross price elasticity of demand (Epo) is given
by:
% Q
Q / Q
0
P 
0 
% P
P 0 / P 0
E
Where Q is the quantity of the good (X) and P0 is
the price of of a related good or service( good Y)
•If EP0 > 0, then X and Y are substitutes—that is, an increase in the
price of good Y will result in an increase in the demand for good X
•If EP0 < 0, then X and Y are complements—that is, an increase in the
price of good Y will result in a decrease in the demand for good X
Price Elasticity Changes Along a Linear Demand
Curve
Price
$ 400
300
Demand tends to be
elastic at higher
prices and inelastic
at lower prices
Demand is
price elastic
A
Elasticity = -1
M
200
100
0
Marginal
revenue
MR = 400 -.5Q
400
Demand is
price inelastic
B
P = 400 - .25Q
800
1,200
1,600
Quantity Demanded
(a)
Revenue rule
Revenue rule: When demand is elastic, price
and revenue move inversely. When demand is
inelastic, price and revenue move together.
As price falls along the elastic
portion of the demand curve
(price above $200), revenue
will increase; whereas as price
falls along the inelastic portion
(below $200), revenue will
decrease
Notice the Marginal Revenue
(MR) function dips below the
horizontal axis at Q = 800.
Revenue
$ 160,000
120,000
Total revenue
R = 4 00Q -.2 5Q2
0
400
800
1,200
Quantity Demanded
(b)