Cross Price Elasticity
of Demand
IB Economics
Cross Price Elasticity of
Demand (PEDx,y)
• Cross price elasticity (PEDx,y) measures
the responsiveness of demand for good X
following a change in the price of good Y.
• In effect we are measuring to which
degree a good is a substitute or
complement
• PEDx,y describes the important distinction
between substitutes and complements
quantitatively.
Formula for PEDx,y
Qx1  Qx0
PEDx , y
100
Q x0
% in Qd for X


Py1  Py0
% in Price of Y
100
Py0
Example
•
•
1GB flash cards go down in price
from $250 to $165
Qx1  Qx0
PEDx , y
MP3 players demanded goes up
from 13’000 to 18’000 in the same
time period.
100
Q x0
% in Qd for X


Py1  Py0
% in Price of Y
100
Py0
Qx1  Qx0
PEDx , y
Q x0

Py1  Py0
Py0
•
X = MP3 players, Y = flash cards
Qx1  Qx0
PEDx , y
Qx0

Py1  Py0
Py0
•
-1.13 tells us the goods are fairly
complementary
18'000  13'000
100
13
'
000

165  250
100
100
250
100
18'000  13'000
 100
0.385
13'000


 1.13
165  250

0
.
34
 100
 100
250
 100
Cross Elasticity of Demand
(PEDx,y) – Substitutes
• Substitutes:
– With substitute goods such as brands of
razors, an increase in the price of one good
will lead to an increase in demand for the
rival product
– Cross price elasticity will be positive
– Weak substitutes – low PEDx,y
– Close substitutes – high PEDx,y
Cross Elasticity of Demand
(PEDx,y) - Complements
• Complements:
– Goods that are in complementary demand
– The cross price elasticity of demand for two
complements is negative
– Weak complements – low PEDx,y
– Close complements – high PEDx,y
• Note the higher the magnitude (ignoring the sign) the closer the
complement.
Substitutes and Complements
Price of
Good S
Two Weak Substitutes
Demand
Goods S and T are weak
substitutes
P2
A substantial rise in the price
of Good S leads to a relatively
small rise in the demand for
good T
P1
The cross price elasticity of
demand will be positive but
the coefficient of elasticity will
be less than one
Quantity demanded of
Good T
Substitutes and Complements
Two Close Complements
Goods X and Y are close
complements
A fall in the price of good X
leads to relatively large rise in
the demand for good Y
The cross price elasticity of
demand will be negative and
the coefficient of elasticity will
be more than one
Price of
Good X
Deman
d
P1
P2
Complements are said to be
in JOINT DEMAND
Q1
Q2
Quantity demanded of
Good Y
Exercise
• Given that the price of Xbox 360®
decreases due to a technological advance
(lower productivity costs) what will happen
to the demand for games for Xbox® and
Playstation 3® consoles?
• Can you analyse the situation
economically, drawing XED diagrams and
supply/ demand diagrams to illustrate your
conclusions?
XBox
Price increase for Xbox games
(negative: complements)
Price of
Xbox
Price
Xbox
games
S
D2
D1
Quantity of Xbox
games
Quantity of Xbox
games
XBox
Price increase for Xbox games
(positive: substitutes)
Price of
Xbox
Price PS3
S
D1
D2
Quantity of PS3
Quantity of PS3
Any other comments?
Goods with zero cross-price elasticity of demand
Price of
Good A
Demand
No correlation between A & B
A fall in the price of good A
leads to no change in the
demand for good B
P1
Therefore the cross-price
elasticity of demand is zero
P2
e.g.
Cheese and Caribbean
Holidays
P3
Quantity demanded of
Good B
Cross Price Elasticity for Substitutes*
Product
Coca Cola
Camembert Cheese
Train journey from
Paris to Geneva
Dowe Egberts Filter
Coffee
Ticket to a film at the
REX Cinema in
Vevey
Close
Substitute
Weak
Substitute
Good with no
relationship
Complementary Goods
Product
Personal
Computer
A bottle of
expensive
white wine
Short Break
Weekend in
Barcelona
Close
Complement
Weak
Complement
Good with no
relationship
Importance of PEDx,y for
businesses
• Pricing strategies for substitutes:
– Consider for example the cross-price effect that has occurred with the rapid
expansion of low-cost airlines in the European airline industry.
• Pricing strategies for complementary goods:
• For example, popcorn, soft drinks and cinema tickets have a high negative
value for cross price elasticity– they are strong complements.
• Advertising and marketing:
• In highly competitive markets between brand names carry substantial value,
many businesses spend huge amounts of money every year on persuasive
advertising and marketing.
Importance of PEDx,y for
businesses
•
Pricing strategies for substitutes: If a competitor cuts the price of a rival product, firms use estimates of cross-price
elasticity to predict the effect on the quantity demanded and total revenue of their own product. For example, two
or more airlines competing with each other on a given route will have to consider how one airline might react to its
competitor’s price change. Will many consumers switch? Will they have the capacity to meet an expected rise in
demand? Will the other firm match a price rise? Will it follow a price fall?
•
Consider for example the cross-price effect that has occurred with the rapid expansion of low-cost airlines in the
European airline industry. This has been a major challenge to the existing and well-established national air
carriers, many of whom have made adjustments to their business model and pricing strategies to cope with the
increased competition.
•
Pricing strategies for complementary goods: For example, popcorn, soft drinks and cinema tickets have a high
negative value for cross price elasticity– they are strong complements. Popcorn has a high mark up i.e. pop corn
costs pennies to make but sells for more than a pound. If firms have a reliable estimate for PEDx,y they can
estimate the effect, say, of a two-for-one cinema ticket offer on the demand for popcorn. The additional profit from
extra popcorn sales may more than compensate for the lower cost of entry into the cinema.
•
Advertising and marketing: In highly competitive markets where brand names carry substantial value, many
businesses spend huge amounts of money every year on persuasive advertising and marketing. There are many
aims behind this, including attempting to shift out the demand curve for a product (or product range) and also build
consumer loyalty to a brand. When consumers become habitual purchasers of a product, the cross price elasticity
of demand against rival products will decrease. This reduces the size of the substitution effect following a price
change and makes demand less sensitive to price. The result is that firms may be able to charge a higher price,
increase their total revenue and turn consumer surplus into higher profit.