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

100

100

Y of Pricein %

Xforin%

0

01

0

01

,

y

yy

x

xx

dyx

P

PP

Q

QQ

QPED

Example• 1GB flash cards go down in price

from $250 to $165

• MP3 players demanded goes up from 13’000 to 18’000 in the same time period.

• X = MP3 players, Y = flash cards

• -1.13 tells us the goods are fairly complementary

100

100

Y of Pricein %

Xforin%

0

01

0

01

,

y

yy

x

xx

dyx

P

PP

Q

QQ

QPED

100250

250165

100000'13

000'13000'18

100

100

0

01

0

01

,

y

yy

x

xx

yx

P

PP

Q

QQ

PED

13.134.0

385.0

100250

250165

100000'13

000'13000'18

100

100

0

01

0

01

,

y

yy

x

xx

yx

P

PP

Q

QQ

PED

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 ComplementsPrice of Good S

Quantity demanded of Good T

Demand

Two Weak Substitutes

P1

P2

Goods S and T are weak substitutes

A substantial rise in the price of Good S leads to a relatively small rise in the demand for good T

The cross price elasticity of demand will be positive but the coefficient of elasticity will be less than one

Substitutes and Complements

Price of Good X

Quantity demanded of Good Y

Demand

Two Close Complements

P2

P1

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

Complements are said to be in JOINT DEMAND

Q1 Q2

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

Quantity of Xbox games

Quantity of Xbox games

Price Xbox games

S

D2

D1

XBox

Price increase for Xbox games

(positive: substitutes)

Price of Xbox

Quantity of PS3 Quantity of PS3

Price PS3S

D1

D2

Any other comments?

Goods with zero cross-price elasticity of demand

Price of Good A

Quantity demanded of Good B

Demand

P1

P2

P3

No correlation between A & B

A fall in the price of good A leads to no change in the demand for good B

Therefore the cross-price elasticity of demand is zero

e.g.

Cheese and Caribbean Holidays

Cross Price Elasticity for Substitutes*

Product Close Substitute

Weak Substitute

Good with no relationship

Coca Cola

Camembert Cheese

Train journey from Paris to Geneva

Dowe Egberts Filter Coffee

Ticket to a film at the REX Cinema in

Vevey

Complementary GoodsProduct Close

ComplementWeak Complement

Good with no relationship

Personal Computer

A bottle of expensive white wine

Short Break Weekend in Barcelona

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.