1. Income Elasticity of Demand and Cross Price Elasticity of Demand
Module 9
Income Elasticity of Demand and Cross Price Elasticity of Demand

2. Objectives
Define the income elasticity of demand and how to calculate it.
Define the cross-price elasticity of and how to calculate it.

3. Define the income elasticity of demand
Objective 1
Define the income elasticity of demand
and understand how to calculate it.
The income elasticity of demand (εI ) measures the responsiveness of quantity demanded to changes in consumer income. 3

4. Objective 1….the income elasticity of demand
An example will help demonstrate what it is that the income elasticity measures. The graph shows what happens to Janet’s demand for coffee when her income changes.
Example 1: At point “c”, the price of coffee is $3.00, Janet’s income is $500/week and Janet’s quantity demanded is 5 cups.
When her income rises to $700/week, her demand curve shifts right. She is now willing to buy 8 cups, at the same price. This is given by point “w” on the new demand curve D1.

5. Objective 1….the income elasticity of demand
Note: the price of coffee does not change; income changes and Janet responds to the income change by buying more coffee.
Income elasticity is concerned precisely with this: the change from “c” on one demand curve to “w” on another demand curve, holding price constant.

6. Objective 1….the income elasticity of demand
In Example 1, Janet’s quantity demanded increases when her income increases.
To Janet coffee is a normal good.
The income elasticity coefficient for a normal good is positive. 6

7. Objective 1….the income elasticity of demand
Example 2: Consider Daria’s demand for coffee.
At point “c”, the price of coffee is $3.00, Daria’s income is $500/week and Daria’s quantity demanded is 5 cups.
When her income rises to $700/week, she buys less at the same price of coffee. Her quantity demanded has now falls to 3 cups, corresponding to point “x” on the new demand curve D1.

8. Objective 1….the income elasticity of demand
Daria’s quantity demanded decreases when her income increases.
To Daria coffee is an inferior good.
The income elasticity coefficient for an inferior good is negative. 8

9. Objective 1….the income elasticity of demand
The formula for the income elasticity of demand is:
If the income elasticity of demand (εI) is positive, εI > 0  the good is a normal good.
If the income elasticity of demand (εI) is negative, εI < 0  the good is an inferior good.

10. Objective 1….calculating the income elasticity of demand
Example 3: Suppose quantity demanded increases by 4% when income rises by 5%. What is the income elasticity of demand for this good? Indicate if the good is normal or inferior.
Solving the Problem
Apply the elasticity formula:
Since the income elasticity is a positive number, the good is a normal good. 10 10

11. Objective 1….calculating the income elasticity of demand
The income elasticity coefficient = 0.8. What does the number 0.8 mean?
Let’s go back to the elasticity formula and rearrange the
equation by cross multiplying.
The income elasticity formula can be rewritten as:
%∆Quantity Demanded = 0.8 × %∆Income
For every 1% increase in income, quantity demanded increases by 0.8% or for every 10% increase in income, quantity demanded increases by 8%.

12. Objective 1….calculating the income elasticity of demand
Example 4: Suppose when income rises by 10%, quantity demanded decreases by 6%. Calculate the income elasticity of demand for this good. Indicate if the good is normal or inferior.
Solving the Problem
Apply the elasticity formula:
The negative coefficient indicates that the good is an inferior good.

13. Objective 1….calculating the income elasticity of demand
Example 5: Suppose at an income level of $30,000, Francesca buys 2 units of good X per month. When her income rises to $50,000, she buys 5 units per month. Calculate the income elasticity of demand for good X and indicate if the good is inferior or normal.
Solving the Problem
Essentially, you are given two
sets of income-quantity combinations:
“a”: Income0= $30,000, Q0 = 2 and “b”: Income1 = $50,000; Q1 = 5.
Apply these values to the midpoint formula.

14. Objective 1….the average method of calculating the income elasticity of demand
Simplify by cancelling the ½ s and the 100s to give: 14

15. Objective 1….the average method of calculating the income elasticity of demand
Now plug in the given values:
The income elasticity is positive. Therefore, good X is a normal good.

16. Objective 1: …describing income elasticities
If the income elasticity of demand > 1  demand is
income elastic.
If the income elasticity of demand < 1  demand is
Income inelastic.
If the income elasticity of demand = 1  demand is
unit income elastic.

17. Objective 1: …describing income elasticities
Since inferior goods have a negative income elasticity (<0) which also means a number < 1, inferior goods are income inelastic ALWAYS.
Normal goods may be income elastic or income inelastic.
Necessities are normal goods that are income inelastic.
The income elasticity is a positive number less than 1.
Luxury goods are normal goods that are income elastic
The income elasticity is a positive number greater than 1.

18. Objective 1: Income elasticity – a summary
Income elasticity of demand > 1
Normal, luxury good
Income elastic
Income elasticity of demand is
a positive number less than 1.
Normal, necessity
Income inelastic
Income elasticity = 1
Normal
Unit income elastic
Income elasticity of demand is a
a negative number.
Inferior good

19. Objective 1: Income elasticity – a summary
The income elasticity of demand tells us how quantity demanded responds to changes in income.
The income elasticity of demand is used to determine if a good is an inferior good or a normal good and, if it is a normal good, whether it is it luxury good or a necessity. 19

20. Define the cross-price elasticity of demand ….
Objective 2
Define the cross-price elasticity of demand ….
The cross price elasticity of demand (CPE) measures the responsiveness of quantity demanded to changes in the price of a substitute good or a complementary good, holding all else constant.
For example, if the price of coke changes, how does this affect the quantity demanded of Pepsi, holding the price of Pepsi constant?
Or, if the price of bagels changes, how does this affect the quantity demanded of cream cheese, holding the price of cream cheese constant? 20

21. Objective 2….the cross-price elasticity of demand
An example will help demonstrate what it is that the
cross-price elasticity measures.
Example 1: Consider two goods, good X and good Y.
Suppose the price of good X rises from $6 to $7.
The increase is the price of good X is demonstrated by a movement along the demand curve for good X.
When price rises, there is a movement along the curve

22. Objective 2….the cross-price elasticity of demand
As a result of the increase in the price of good X, the demand for good Y increases.
At a given price of good Y, the quantity demanded increases from Qe to Qf.

23. Objective 2….the cross-price elasticity of demand
Note: the price of good Y does not change; the price of good X has changed and the consumer responds to this change by buying more of good Y.
Cross price elasticity elasticity is concerned precisely with this: the change in the price in market X and its effect on the quantity demanded in market Y. In market Y quantity demanded has changed from “e” on one demand curve to “f” on another demand curve, holding the price of good Y constant. 23

24. Objective 2….the cross-price elasticity of demand
In my example, the increase in the price of good X causes an increase in the quantity demanded of good Y.
 there is a positive relationship between the change in the price of X and the change in the quantity
demanded of Y.
 X and Y are substitute goods.

25. Objective 2….understanding the cross-price elasticity of demand
Example: the cross price elasticity between the price of Coke and the quantity demanded of Pepsi.
Suppose Price of Coke ↑
 Demand for Pepsi increases (shifts right).
At a given price of Pepsi, quantity demanded of
Pepsi increases.
 positive relationship between the price of Coke and
the quantity demanded of Pepsi.
 Coke and Pepsi are substitutes.

26. Objective 2….the cross-price elasticity of demand
Example 2: Consider two goods, good A and good B.
Suppose the price of good A rises from $5 to $6.
The increase is the price of good A is demonstrated by a movement along the demand curve for good A.
When price rises, there is a movement along the curve

27. Objective 2….the cross-price elasticity of demand
As a result of the increase in the price of good A, the demand for good B decreases.
At a given price of good Y, the quantity demanded decreases from Qg to Qh. 27

28. Objective 2….the cross-price elasticity of demand
In this example, the increase in the price of good A causes a decrease in the quantity demanded of good B.
 there is a negative relationship between the change in the price of good A and the change in the quantity
demanded of good B.
 A and B are complementary goods.

29. Objective 2….understanding the cross-price elasticity of demand
Example: the cross price elasticity between the price of donuts and the quantity demanded of coffee.
Suppose Price of donuts ↑
 demand for coffee decreases (shifts left). At a given price of coffee, quantity demanded of coffee decreases.
 negative relationship between the price of donuts and
the quantity demanded of coffee.
 donuts and coffee are complements.

30. Objective 2…. the cross-price elasticity of demand
Let CPEXY denote the cross price elasticity of demand between good X and good Y.
The formula for the cross price elasticity of demand is:
CPEXY
If the cross price elasticity of demand is positive,
CPEXY > 0  X and Y are substitutes.
If the cross price elasticity of demand is negative,
CPEXY < 0  X and Y are complements.

31. Objective 2: calculating the cross-price elasticity of demand
Example 3: Suppose a 6 percent decrease in the price of ibuprofen causes a 10 percent decrease in the quantity demanded of Tylenol. What is the cross price elasticity of demand for Ibuprofen with respect to the price of Tylenol? Are the two goods complements or substitutes?

32. Objective 2: calculating the cross-price elasticity of demand
Example 3: Suppose a 6 percent decrease in the price of ibuprofen causes a 10 percent decrease in the quantity demanded of Tylenol. What is the cross price elasticity of demand for Ibuprofen with respect to the price of Tylenol? Are the two goods complements or substitutes?
Solving the Problem
Apply the formula: 32

33. Objective 2: calculating the cross-price elasticity of demand
Example 3: Suppose a 6 percent decrease in the price of ibuprofen causes a 10 percent decrease in the quantity demanded of Tylenol. What is the cross price elasticity of demand for Ibuprofen with respect to the price of Tylenol? Are the two goods complements or substitutes?
Solving the Problem
Apply the formula:
The coefficient is positive which indicates that Tylenol and Ibuprofen are substitutes. 33

34. Objective 2: understanding the cross-price elasticity of demand
How do we interpret the number 1.67≈ 1.7?
The cross price elasticity formula can be rewritten as follows:
%∆Quantity Demanded of Tylenol = 1.7 x %∆ Price of Ibuprofen
For every 1% decrease in the price of ibuprofen, the quantity demanded of Tylenol falls by 1.7% or, for every for every 10% increase in the price of ibuprofen, the quantity demanded of Tylenol rises by 17%.

35. Objective 2: calculating the cross-price elasticity of demand
Example 4: In the graph, the demand for tortilla chips has shifted outward because the price of salsa has fallen from $3.20 to $2.80 per package. Calculate the cross-price elasticity of demand between tortilla chips and salsa.
What is the relationship between these two goods?

36. Objective 2: calculating cross-price elasticity
Solving the problem:
To calculate the cross-price elasticity of demand between tortilla chips and salsa, we have to calculate
(1) the percentage change in the quantity demanded of tortilla chips
(2) the percentage change in the price of salsa
(3) apply the average or midpoint method of calculating elasticities 36

37. Objective 2: calculating cross-price elasticity
Solving the problem:
To calculate the cross-price elasticity of demand between tortilla chips and salsa, we have to calculate
(1) the percentage change in the quantity demanded of tortilla chips
(2) the percentage change in the price of salsa
(3) apply the average or midpoint method of calculating elasticities
The percentage change in the quantity demanded of tortilla chips
The percentage change in the price of salsa 37

38. Objective 2: calculating cross-price elasticity
Solving the problem:
To calculate the cross-price elasticity of demand between tortilla chips and salsa, we have to calculate
(1) the percentage change in the quantity demanded of tortilla chips
(2) the percentage change in the price of salsa
(3) apply the average or midpoint method of calculating elasticities
The percentage change in the quantity demanded of tortilla chips
The percentage change in the price of salsa 38

39. The average method of calculating cross price elasticity:39

40. The average method of calculating cross price elasticity:
The negative coefficient indicates that the two goods are complements.

41. Objective 1: Cross Price elasticity – a summary
The cross price elasticity of demand between good X and good Y tells us how quantity demand of good Y responds to a change in the price of good X 41

42. Objective 1: Cross Price elasticity – a summary
The cross price elasticity of demand between good X and good Y tells us how quantity demand of good Y responds to a change in the price of good X
The important thing to note is that we are looking at price changes in one market and quantity changes in another market. 42

43. Objective 1: Cross Price elasticity – a summary
The cross price elasticity of demand between good X and good Y tells us how quantity demand of good Y responds to a change in the price of good X
The important thing to note is that we are looking at price changes in one market and quantity changes in another market.
The sign of cross price elasticity of demand coefficient indicates if the two goods are substitutes or complements. 43

44. Objective 1: Cross Price elasticity – a summary
Cross price elasticity of demand between X and Y is a positive number.
X and Y are substitutes
Cross price elasticity of demand between X and Y is a negative number.
X and Y are complements
Cross price elasticity of demand between X and Y is zero.
X and Y are unrelated