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

Module 9Module 9Income Elasticity of

Demand and Cross Price Elasticity of Demand

Income Elasticity of Demand and Cross Price

Elasticity of Demand

1

Define the income elasticity of demandincome elasticity of demand and how to calculate it.

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ObjectivesObjectives

Define the income elasticity of demandincome elasticity of demand and how to calculate it.

Define the cross-price elasticitycross-price elasticity of demand and how to calculate it.

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ObjectivesObjectives

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Define the income elasticity of demandDefine the income elasticity of demandand understand how to calculate it.and understand how to calculate it.

Objective 1Objective 1

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Define the income elasticity of demandDefine the income elasticity of demandand understand how to calculate it.and understand how to calculate it.

The income elasticity of demandincome elasticity of demand (εI ) measures the responsiveness of quantity demanded to changes in consumer income.


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Objective 1….the income elasticity of demandObjective 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.

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Example 1:Example 1: At point “c”,“c”, the price of coffee is $3.00, Janet’s income is $500/week and Janet’s quantity demanded is 5 cups.

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Example 1:Example 1: At point “c”,“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”“w” on the new demand curve Dnew demand curve D11.

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Note: the price of coffee does not change; income changes and Janet responds to the income change by buying more coffee.


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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.


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In Example 1, Janet’s quantity demanded increasesincreases when her income increasesincreases.


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To Janet coffee is a normal good.normal good.


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To Janet coffee is a normal good.normal good.

The income elasticity coefficient for a normal good is positive.positive.


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Example 2:Example 2: Consider Daria’s demand for coffee.

At point “c”,“c”, the price of coffee is $3.00, Daria’s income is $500/week and Daria’s quantity demanded is 5 cups.


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Example 2:Example 2: Consider Daria’s demand for coffee.

At point “c”,“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 risesincome rises to $700/week, she buys lessshe buys less at the same price of coffee. Her quantity demanded has now falls to 3 cups, corresponding to point “x”“x” on the new demand curve DD11..


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Daria’s quantity demanded decreasesdecreases when her income increases.increases.


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To Daria coffee is an inferiorinferior good.


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To Daria coffee is an inferiorinferior good.

The income elasticity coefficient for an inferior good is negative.negative.


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ΔΔ

% Quantity DemandedIncome Elasticity of Demand = % Income


The formula for the income elasticity of demand is:

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ΔΔ


If the income elasticity of demand (εI) is positive,positive, εI > 0 the good is a normal goodnormal good.



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ΔΔ


If the income elasticity of demand (εI) is positive,positive, εI > 0 the good is a normal goodnormal good.

If the income elasticity of demand (εI) is negativenegative, εI < 0 the good is an inferiorinferior good.



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Example 3: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.

Objective 1….calculating the income elasticity of Objective 1….calculating the income elasticity of demanddemand

10

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Since the income elasticity is a positive number, the good is a normal good.

10

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ΔΔ


4=5

= 0.8


Solving the ProblemSolving the Problem

Apply the elasticity formula:


Since the income elasticity is a positive number, the good is a normal good.

10

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The income elasticity coefficient = 0.8. What does the number 0.8 mean?

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Let’s go back to the elasticity formula and rearrange the equation by cross multiplying.

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The income elasticity formula can be rewritten as:

%∆Quantity Demanded = 0.8 × %∆Income




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The income elasticity formula can be rewritten as:

%∆Quantity Demanded = 0.8 × %∆Income

For every 1% increaseincrease in income, quantity demanded increasesincreases by 0.8%, or for every 10% increase in income, quantity demanded increases by 8%.




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Example 4: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.

Objective 1….calculating the income elasticity Objective 1….calculating the income elasticity of demandof demand

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The negative coefficient indicates that the good is an inferior good. inferior good.


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Apply the elasticity formula:

The negative coefficient indicates that the good is an inferior good. inferior good.


ΔΔ


6=10

= 0.6

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Example 5: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.


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Example 5: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.



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 midpoint formula. formula.

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Simplify by cancelling the ½ s and the 100s to give:

ΔΔ

Δ

Δ0 1

0 1

× +

=×

+

% Quantity Income Elasticity of Demand = % Income

Quantity 100½(Q Q )

Income 100½(I I )

Objective 1….the average method of calculating the Objective 1….the average method of calculating the income elasticity of demandincome elasticity of demand

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Simplify by cancelling the ½ s and the 100s to give:

ΔΔ

Δ

Δ0 1

0 1

× +

=×

+

% Quantity Income Elasticity of Demand = % Income

Quantity 100½(Q Q )

Income 100½(I I )

Δ Δ

0 1

0 1

0 1

0 1

0 1

0 1

0 1

0 1

0 1

0 1

Quantity IncomeIncome Elasticity of Demand = ÷

(Q + Q ) (I + I )

(Q - Q ) (I - I )=

(Q + Q ) (I + I )

Q - Q I + I= ×

Q + Q I - I


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Now plug in the given values:

0 1

0 1

0 1

0 1

Q - Q I + IIncome Elasticity of Demand = ×

Q + Q I - I

2 - 5 30,000 + 50,000= ×

2 + 5 30,000 - 50,000

-3 80,000= ×

7 -20,000

3 8= ×

7 2= 1.71


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Now plug in the given values:

The income elasticity is positive. Therefore, good X is a normal normal good.

0 1

0 1

0 1

0 1

Q - Q I + IIncome Elasticity of Demand = ×

Q + Q I - I

2 - 5 30,000 + 50,000= ×

2 + 5 30,000 - 50,000

-3 80,000= ×

7 -20,000

3 8= ×

7 2= 1.71


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Objective 1: …describing income elasticitiesObjective 1: …describing income elasticities

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If the income elasticity of demand > 1 demand is income elastic.income elastic.


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If the income elasticity of demand < 1 demand is Income Income

inelastic.inelastic.


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If the income elasticity of demand < 1 demand is Income Income

inelastic.inelastic.

If the income elasticity of demand = 1 demand is unit income unit income

elastic.elastic.


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Since inferiorinferior goods have a negative income elasticity (<0) which also means a number < 1, inferior goods are income income inelastic ALWAYS.inelastic ALWAYS.


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NormalNormal goods may be income elastic or income inelastic.


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NecessitiesNecessities are normal goods that are income inelastic.The income elasticity is a positive number less than 1positive number less than 1.


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NecessitiesNecessities are normal goods that are income inelastic.The income elasticity is a positive number less than 1positive number less than 1.

Luxury goodsLuxury goods are normal goods that are income elasticThe income elasticity is a positive number greater than 1.positive number greater than 1.


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Income elasticity of demand > 1> 1 Normal, luxury good Income elasticelastic

Objective 1: Income elasticity – a summaryObjective 1: Income elasticity – a summary

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Income elasticity of demand is a positive number less than 1.positive number less than 1.

Normal, necessity Income inelasticinelastic


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Income elasticity = 1= 1 Normal UnitUnit income elastic


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Income elasticity = 1= 1 Normal UnitUnit income elastic

Income elasticity of demand is a a negative number.negative number. Inferior good Income inelasticinelastic


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The income elasticity of demandincome elasticity of demand tells us how quantity demanded responds to changes in income.


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The income elasticity of demandincome 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 inferiorinferior good or a normalnormal good and, if it is a normal good, whether it is it luxury luxury good or a necessitynecessity.


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The cross price elasticity of demandcross price elasticity of demand (CPE) measures the responsiveness of quantity demanded to changes in the price of a substitutesubstitute good or a complementarycomplementary good, holding all else constant.

Define the cross-price elasticity of demand ….Define the cross-price elasticity of demand ….


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For example, if the price of coke changes, how does this affect the quantity demanded of Pepsi, holding the price of Pepsi constant?



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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?



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Example 1:Example 1: Consider two goods, good X and good Y. Suppose the price of good X rises from $6 to $7.

Objective 2….the cross-price elasticity of demandObjective 2….the cross-price elasticity of demand

An example will help demonstrate what it is that the cross-price elasticity measures.

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Example 1:Example 1: Consider two goods, good X and good Y. Suppose the price of good X rises from $6 to $7.


An example will help demonstrate what it is that the cross-price elasticity measures.

The increase is the price of good X is demonstrated by a movementmovement along the demand curve for good X.

When price rises, there is a movement along the curve

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As a result of the increase in the price of good Xprice of good X, the demand for good Y increasesgood Y increases.


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As a result of the increase in the price of good Xprice of good X, the demand for good Y increasesgood Y increases.

At a given price of good Y, the quantity demandedquantity demanded increasesincreases from QQee

to QQff..


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Note: the price of goodprice of good YY does not not change; the price of good X has changed and the consumer responds to this change by buying more of good Y.


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Note: the price of goodprice of good YY does not 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 elasticityCross 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.


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In my example, the increaseincrease in the price of good Xprice of good X causes an increaseincrease in the quantity demanded of good Yquantity demanded of good Y.


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there is a positive relationshippositive relationship between the change in the price of X and the change in the quantity demanded of Y.


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there is a positive relationshippositive relationship between the change in the price of X and the change in the quantity demanded of Y.

X and Y are substitute goods.substitute goods.


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Example:Example: the cross price elasticity between the price of Coke and the quantity demanded of Pepsi.

Objective 2….understanding the cross-price elasticity of Objective 2….understanding the cross-price elasticity of demanddemand

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Suppose Price of Coke ↑Price of Coke ↑

Demand for Pepsi increases (shifts right). At a given price of Pepsi, quantity demanded of Pepsi increases.


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positive relationshippositive relationship between the price of Coke and the quantity demanded of Pepsi.


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positive relationshippositive relationship between the price of Coke and the quantity demanded of Pepsi.

Coke and Pepsi are substitutes.substitutes.


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Example 2:Example 2: Consider two goods, good A and good B. Suppose the price of good A rises from $5 to $6.


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Example 2: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 movementmovement along the demand curve for good A.


When price rises, there is a movement along the curve

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As a result of the increase in the price of good Aprice of good A, the demand for good B decreasesgood B decreases.


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As a result of the increase in the price of good Aprice of good A, the demand for good B decreasesgood B decreases.

At a given price of good Y, the quantity demandedquantity demanded decreasesdecreases from QQgg

to QQhh..


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In this example, the increaseincrease in the price of good A price of good A causes a decreasedecrease in the quantity demanded of good Bquantity demanded of good B.


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there is a negative relationshipnegative relationship between the change in the price of good A and the change in the quantity demanded of good B.


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there is a negative relationshipnegative 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.complementary goods.


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Example:Example: the cross price elasticity between the price of donuts and the quantity demanded of coffee.

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Suppose Price of donuts ↑Price of donuts ↑

demand for coffee decreases (shifts left). At a given price of coffee, quantity demanded of coffee decreases.

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negative relationshipnegative relationship between the price of donuts and the quantity demanded of coffee.

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negative relationshipnegative relationship between the price of donuts and the quantity demanded of coffee.

donuts and coffee are complements.complements.

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The cross price elasticitycross 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

Objective 1: Cross Price elasticity – a summaryObjective 1: Cross Price elasticity – a summary

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The important thing to note is that we are looking at price changes in one marketprice changes in one market and quantity changes in quantity changes in another market.another market.


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The signsign of cross price elasticity of demand coefficient indicates if the two goods are substitutessubstitutes or complements.complements.


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Let CPECPEXYXY denote the cross price elasticity of demand between good X and good Y.

Objective 2…. the cross-price elasticity of demandObjective 2…. the cross-price elasticity of demand

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ΔΔ

% Quantity Demanded of Good Y= % Price of Good XCPEXY


The formula for the cross price elasticity of demand is:


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ΔΔ




If the cross price elasticity of demand is positive,positive, CPEXY > 0 X and Y are substitutes.substitutes.


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ΔΔ




If the cross price elasticity of demand is positive,positive, CPEXY > 0 X and Y are substitutes.substitutes.

If the cross price elasticity of demand is negativenegative,CPEXY < 0 X and Y are complements.complements.


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Example 3:Example 3: Suppose a 6 percent decreasedecrease in the price of ibuprofen causes a 10 percent decrease 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?

Objective 2: calculating the cross-price elasticity Objective 2: calculating the cross-price elasticity of demandof demand

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ΔΔ

% Quantity Demanded of Tylenol CPE = % Price of Ibuprofen

-10=-6

=1.67



Apply the formula:

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ΔΔ

% Quantity Demanded of Tylenol CPE = % Price of Ibuprofen

-10=-6

=1.67

The coefficient is positivepositive which indicates that Tylenol and Ibuprofen are substitutes.substitutes.



Apply the formula:

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How do we interpret the number 1.67≈ 1.7?How do we interpret the number 1.67≈ 1.7?

Objective 2: understanding the cross-price elasticity of Objective 2: understanding the cross-price elasticity of demanddemand

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The cross price elasticity formula can be rewritten as follows:

%∆Quantity Demanded of Tylenol = 1.7 x %∆ Price of Ibuprofen


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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%.


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Example 4:Example 4: In the graph, the demand fordemand for tortilla chipstortilla chips has shifted outward because the price of salsaprice 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?

Objective 2: calculating the cross-price Objective 2: calculating the cross-price elasticity of demandelasticity of demand

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Solving the problem: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

Objective 2: calculating cross-price elasticityObjective 2: calculating cross-price elasticity

The percentage change in the quantity demanded of tortilla chips

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tortilla chips(2) the percentage change in the price of salsa


The percentage change in the price of salsa


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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 price of salsa


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

c a

0 1

c

%ΔQuantity Demanded of Tortilla ChipsCross Price Elasticity

%ΔPrice of Salsa

ΔQuantity Demanded of Tortilla Chips × 100

½(Q + Q )ΔPrice of Salsa

× 100½(P + P )

ΔQuantity Demanded of Tortilla Chips(Q + Q

=

=

= a

0 1

2,000 -0.4 = ÷

24,000 6

1 6 = - ×

12 0.4

= -1.25

)

ΔPrice of Salsa

(P + P )

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

c a

0 1

c

%ΔQuantity Demanded of Tortilla ChipsCross Price Elasticity

%ΔPrice of Salsa

ΔQuantity Demanded of Tortilla Chips × 100

½(Q + Q )ΔPrice of Salsa

× 100½(P + P )

ΔQuantity Demanded of Tortilla Chips(Q + Q

=

=

= a

0 1

2,000 -0.4 = ÷

24,000 6

1 6 = - ×

12 0.4

= -1.25

)

ΔPrice of Salsa

(P + P )

The negative coefficient indicates that the two goods are complementscomplements.

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The signsign of cross price elasticity of demand coefficient indicates if the two goods are substitutessubstitutes or complements.complements.


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Cross price elasticity of demand between X and Y is a positivepositive number. X and Y are substitutessubstitutes


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Cross price elasticity of demand between X and Y is a negative negative number. X and Y are complementscomplements


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Cross price elasticity of demand between X and Y is a negative negative number. X and Y are complementscomplements

Cross price elasticity of demand between X and Y is zero.zero. X and Y are unrelatedunrelated


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

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