outline airline ticket pricing the demand function determinants of demand elasticity of demand price...
TRANSCRIPT
Outline
•Airline ticket pricing
•The demand function
•Determinants of demand
•Elasticity of demand
•Price elasticity, revenue, and marginal revenue
Airline ticket pricingConsider 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
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.
Q is the dependent variable; P, PO, and Y are the independent or explanatory variables.
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 Price
290
240
142100 622580
P = 290- Q/2
Quantity of Units Sold
219
Remember that as we move along the demand curve we hold “all other things” constant. In our
case this means Y and PO
Shifts of the demand curve
Price
290
240
142100 622580
P = 290- Q/2
P = 311- Q/2
Quantity of Units Sold
$311
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
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.
ElasticityIssue: 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:
EP =% change in Q
% change in P
001
001
0
0
/)(
/)(
/
/
PPP
QQQ
PP
[3.1]
Example
Price
0Output
P = 290 – Q/2
240
235
100 110
Question: What is EP in the range of demand curve between fares of $240 to $235? To find out:
8.4%1.2
%10
240/)240235(
100/)100110(
pE
Meaning, a 1% increase in fares will result in a 4.8% decrease in passengers per flight (and vice-versa).
A
B
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
Q
P
dP
dQ
PdP
QdQEP
/
/[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 price-quantity point .
Arc elasticity
To compute arc elasticity, or “average” elasticity between two price-quantity points on the demand curve:
2/)(
2/)(/
/
10
10
PPPQQQ
PP
QQEP
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 demandPrice
50
Quantity
100 150 200 250
10
30
20
50
40
70
60
80
90
$100
EP = 0
0
Buyers are absolutely non-responsive to a change in price
Perfectly elastic demand
EP = - infinity
Price
50Quantity
100 150 200 250
1
3
2
5
4
7
6
8
9
$10
(b) Perfectly Elastic Demand
0
In this case, if the price rises a
penny above $5, quantity-
demanded falls to zero.
Income elasticity
Issue: Is demand for a good or service sensitive to a change in consumer income, ceteris paribus?
YY
Y
QEY
/
/
%
%
Income elasticity of demand (EY) is given by:
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 elasticityCross price elasticity of demand (Epo) is given by:
000
0
/
/
%
%
PP
P
QPE
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
$ 400
300
200
100
400 1,200 ,1 600
Quantity Demanded
Price
800
Marginalrevenue
Demand isprice elastic
Demand isprice inelastic
B
M
A
Elasticity = -1
MR = 400 - .5QP = 400 - .25Q
0
(a)
Demand tends to be elastic at higher prices and inelastic at lower prices
Revenue ruleRevenue 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
$ 160,000
120,000
400 1,200Quantity Demanded
Revenue
800
(b)
Total revenueR = 4 0 0 Q - .2 5 Q 2
0
Notice the Marginal Revenue (MR) function dips below the horizontal axis at Q = 800.