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Cross Price Elasticity of Demand (XED)

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Cross Price Elasticity of Demand (XED)

IB Economics

- Outline the concept of cross-price elasticity of demand
- Calculate XED
- Substitute vs. Complementary goods
- Value of XED
- Examine the implications of XED for businesses if prices of substitutes or complements change.

- XED is a measure of the responsiveness of consumers of one good to a change in the price of a related good.
- Measure of how much the demand for a product changes when there is a change in the price of another product.

% D Qty Demanded of good X

FORMULA =

% D Price of good Y

Percent change in quantity demanded / Percent change in price

With cross price elasticity we make an important distinction between substitute products and complementary goods and services.

- Is one for which demand will increase when the price of another good increases.
- Demand for a substitute good will decrease when the price of its substitute decreases.
- How responsive are the consumers of one to a change in the price of the other?
- Example: Beef vs. Chicken

Market demand

(tonnes 000s)

700

Point

Price

(per kg)

20

A

Price (per kg)

A

D

Quantity (tonnes: 000s)

Market demand

(tonnes 000s)

700

500

Point

Price

(per kg)

20

40

A

B

Price (per kg)

B

A

D

Quantity (tonnes: 000s)

Demand for beef

D0

D1

Increase in the price of chicken, increases the demand for beef

P

Price

O

Q0

Q1

Quantity

- Goods that are typically consumed together
- Demand for one is decreased by the price increase of the other
- How responsive are the consumers of one to a change in the price of the other?
- Example: Cameras vs. Memory Cards

Increase in price of cameras

D

Price

P2

P1

O

Q2

Q1

Quantity

Demand for Memory Cards

D1

D0

P

Price

O

Q0

Q1

Quantity

- The owners of a pizza stand find that when their competitor, a hamburger stand, lowers the price of a burger from $2 to $1.80, the number of pizza slices that they sell each week falls from 400 to 380, because of the lower priced burger. Calculate XED.
- XED = -5% / -10% = +0.5

XED may be positive or negative. Sign is important since it tells us what the relationship between the two goods in question is.

- If the value of XED is positive, then the two goods in question may be said to be substitutes for each other.
- If the value of XED is negative, then the two goods in question may be said to be complements for each other.
- If the value of XED is zero, the two goods are unrelated.

XED values and the strength of the relationship between products

XED Value

Negative

Zero

Positive

Weak/Remote Complements

Weak/Remote Substitutes

Close Substitutes

Unrelated Products

Close Complements

Relationship

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

Weak substitutes – inelastic XED

Close substitutes – elastic XED

Cross price elasticity will be positive

+

- Complements:
- Goods that are in complementary demand
- Weak complements – inelastic XED
- Close complements –
elastic XED

- The cross price elasticity of demand for two complements is negative

Cross Elasticity Exercise

- A 10% rise in the price of fish may cause demand for chicken to increase by 2%.
- The fall in the price of paper by 20% causes the demand for pens to increase by 5%.
- A 20% rise in the price of ice cream causes demand for sweets to increase by 4%.
- A 12% fall in the price of air fares leads to a 30% rise in the demand for foreign holidays.
- A 10% rise in bikes will leave the demand for cheese unaffected.

Positive = substitute goods

Negative = complementary

- A 10% rise in the price of fish may cause demand for chicken to increase by 2%. +2% / +10% = +0.2
- The fall in the price of paper by 20% causes the demand for pens to increase by 5%. +5% / -20% = -0.25
- A 20% rise in the price of ice cream causes demand for sweets to increase by 4%. +4% / +20% = +0.2
- A 12% fall in the price of air fares leads to a 30% rise in the demand for foreign holidays. +30% / -12% = -2.5
- A 10% rise in bikes will leave the demand for cheese unaffected.0% / +10% = 0

XED values and the strength of the relationship between products

XED Value

Negative

Zero

Positive

Weak/Remote Complements

Weak/Remote Substitutes

Close Substitutes

Unrelated Products

Close Complements

Relationship

Firms can use XED estimates to predict:

- The impact of a rival’s pricing strategies on demand for their own products:
- Pricing strategies for complementary goods:
- Popcorn and cinema tickets are strong complements. Popcorn has a very high mark up i.e. popcorn costs pennies to make but sells for more than a $1.00
- If firms have a reliable estimate for XED they can estimate the effect, say, of a two-for-one cinema ticket offer on the demand for popcorn

- Effects of the national minimum wage on demand for younger and older workers (might younger workers be replaced?)
- Higher indirect taxes on goods such as tobacco – the impact on demand for nicotine patches and other substitutes

Effect on demand for different modes of mass transport following introduction of road pricing schemes in urban areas

Rise in the price of natural gas – effect on the demand for coal used in power generation

Cross Elasticity Exercise

Additional Exercises

“Light-Bites”, a sandwich shop, finds that when its rival, “Super-Snack”, reduces the price of its chicken wraps from $5 to $4.60, the demand for “Light-Bites” sandwiches falls from 400 sandwiches a week to 340 sandwiches a week. In addition, “Super-Snack” finds that following the fall in price of their chicken wraps, the demand for soft drinks rises from 600 cans to 630 cans per week.

- Calculate the cross elasticity of demand between “Light-Bite” sandwiches and “Super-Snack chicken wraps.
- Explain the relationship above in terms of
cross elasticity of demand.

“Light-Bites”, a sandwich shop, finds that when its rival, “Super-Snack”, reduces the price of its chicken wraps from $5 to $4.60, the demand for “Light-Bites” sandwiches falls from 400 sandwiches a week to 340 sandwiches a week. In addition, “Super-Snack” finds that following the fall in price of their chicken wraps, the demand for soft drinks rises from 600 cans to 630 cans per week.

- Calculate the cross elasticity of demand between “Super-Snack” sandwiches and the “Super-Snack” soft drinks.
- Explain the relationship above in terms of
cross elasticity of demand.