module 8 price elasticity of demand 1. price elasticity of demand, define the price elasticity of...

Module 8Module 8

Price Price ElasticityElasticity of Demand of DemandPrice Price ElasticityElasticity of Demand of Demand

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Define the price elasticity of demandprice elasticity of demand,, understand why it is useful, and how to calculate it.

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ObjectivesObjectives


Understand how to describe elasticities, graph demand curves to represent different elasticities, and understand what happens to elasticity along a linear downward-sloping demand curve.

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Understand how to describe elasticities, graph demand curves to represent different elasticities, and understand what happens to elasticity along a linear downward-sloping demand curve.

Understand the relationship between the price elasticity of demand and total revenue.

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Objective 1: Define the price elasticity of demand, Objective 1: Define the price elasticity of demand, understand why it is useful….understand why it is useful….Objective 1: Define the price elasticity of demand, Objective 1: Define the price elasticity of demand, understand why it is useful….understand why it is useful….

The price elasticity of demandprice elasticity of demand measures the responsiveness of the quantity demanded to changes in price.

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For example, consider the demand curve D1. If price

rises from $10 to $12, quantity demanded falls from Qa to Q1.



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For example, consider the demand curve D1. If price

rises from $10 to $12, quantity demanded falls from Qa to Q1.

If the demand curve is D2,

then when price rises, quantity demanded falls by a smaller amount from Qa

to Q2.



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All elasticity formulas may be stated as fractions or ratios of two percentage change values.

Objective 1: ….how to calculate the price elasticity Objective 1: ….how to calculate the price elasticity of demandof demand

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All elasticity formulas may be stated as fractions or ratios of two percentage change values.

The formula for the price elasticity of demand is:

ΔΔ

% Quantity DemandedPrice Elasticity of Demand = % Price


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Note:Note:

The elasticity formula always uses percentage changesalways uses percentage changes so that the coefficient is not biased by units.


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Note:Note:

The elasticity formula always uses percentage changesalways uses percentage changes so that the coefficient is not biased by units.

Because of the law of demand the sign of the price elasticity of demand is always negative. To simplify interpretation, we will use the absolute valuesabsolute values of the price elasticity of demand and so that the negative sign is ignored.


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Objective 1: calculating the price elasticity of demandObjective 1: calculating the price elasticity of demandObjective 1: calculating the price elasticity of demandObjective 1: calculating the price elasticity of demand

Example 1: Suppose quantity demanded increases by 12% when price rises by 6%. What is the price elasticity of demand?

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12=

6= 2

% Quantity DemandedPrice Elasticity of Demand = % Price

ΔΔ


Example 1: Suppose quantity demanded increases by 12% when price rises by 6%. What is the price elasticity of demand?

Solving the ProblemSolving the Problem

Apply the elasticity formula:

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The price elasticity of demand = 2. What does the number 2 mean?

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

%∆ in Quantity Demanded = |Price Elasticity of Demand| x %∆Price = 2 x %∆Price

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For every 1 percent increase in price, quantity demanded falls by 2 percent,





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For every 1 percent increase in price, quantity demanded falls by 2 percent, or for every 1 percent decrease in price, quantity demanded increases by 2 percent.





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Example 2:Example 2: Suppose when the price of a can of protein powder is $12, quantity demanded is 17 cans. When the price falls to $8, quantity demanded increases to 23 cans. Calculate the price elasticity of demand over this range.


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Essentially, we are given twoprice-quantity combinations:Pa = $12; Qa = 17 and

Pb = $10; Qb = 8

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Essentially, we are given twoprice-quantity combinations:Pa = $12; Qa = 17 and

Pb = $10; Qb = 8

To calculate price elasticity over a range of two prices, we need to apply the average or average or midpoint formula.midpoint formula.

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Objective 1: ..the mid-point formulaObjective 1: ..the mid-point formulaObjective 1: ..the mid-point formulaObjective 1: ..the mid-point formula

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

ΔΔ

Δ

Δ

I I

a b

a b

× +

=×

+

% Quantity DemandededPrice Elasticity of Demand = % Price

Quantity Demanded 100½(Q Q )

Price 100½(P P )

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

ΔΔ

Δ

Δ

I I

a b

a b

× +

=×

+

% Quantity DemandededPrice Elasticity of Demand = % Price

Quantity Demanded 100½(Q Q )

Price 100½(P P )

Δ

Δ

a

a

a b

a b

b b a

a b a b

b a b

a b b a

+

=

+

- -

+ +

- +×

+ -

Quantity Demanded(Q Q )

Price (P P )

Q Q P P=

Q Q P P

Q Q P P=

Q Q P P

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Now plug in the given values:

I I 23 - 17 12 + 8×

23 + 17 12 - 8

20×

4

0.75

Price Elasticity of Demand =

6= 40

=


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Now plug in the given values:

I I 23 - 17 12 + 8×

23 + 17 12 - 8

20×

4

0.75

Price Elasticity of Demand =

6= 40

=


The average elasticity between a and b

is 0.75

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| |dε = the absolute value of the price elasticity of demand

Objective 2Objective 2

Understand how to describe elasticities,…. Understand how to describe elasticities,….

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Δ Δd| ε | > 1 % Quantity demanded > % Price, and demand is price el astic. Δ Δd| ε | > 1 % Quantity demanded > % Price, and demand is price el astic.

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When demand is price elasticprice elastic, the change in quantity demanded is proportionally greater than the change in price.

Δ Δd| ε | > 1 % Quantity demanded > % Price, and demand is price el astic. Δ Δd| ε | > 1 % Quantity demanded > % Price, and demand is price el astic.

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Objective 2: describing elasticities,…. Objective 2: describing elasticities,….

Δ Δd| ε | < 1 % Quantity demanded < % Price, and demand is price inelastic.

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When demand is price inelasticprice inelastic, the change in quantity demanded is proportionally smaller than the change in price.

Δ Δd| ε | < 1 % Quantity demanded < % Price, and demand is price inelastic.

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Δ Δd| ε | = 1 % Quantity demanded = % Price, and demand is unit price inelast ic.


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When demand is unit price elasticunit price elastic, the change in quantity demanded is equal to the change in price.

Δ Δd| ε | = 1 % Quantity demanded = % Price, and demand is unit price inelast ic.


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The polar cases:The polar cases:

Perfectly inelastic demandPerfectly inelastic demand


d| ε | = 0 demand is perf price inelase tctly ic. d| ε | = 0 demand is perf price inelase tctly ic.

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Perfectly inelastic demandPerfectly inelastic demand occurs when a change in price results in no change in quantity demanded.



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Perfectly elastic demandPerfectly elastic demand occurs when a change in price results in an infinite change in quantity demanded.


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Perfectly elastic demandPerfectly elastic demand occurs when a change in price results in an infinite change in quantity demanded.


d| ε | = demand is per price elafect stly ic. d| ε | = demand is per price elafect stly ic.

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Objective 2: graph demand curves to represent Objective 2: graph demand curves to represent different elasticities… different elasticities…


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Quantity demanded does not respond to changes in price. Examples include some types of medication such as insulin for a diabetic.



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Quantity demanded is extremely sensitive to changes in price to the extent that when price rises a tad, quantity demanded falls to zero.



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Quantity demanded is extremely sensitive to changes in price to the extent that when price rises a tad, quantity demanded falls to zero.

In theory, this is the demand curve facing a perfectly competitive firm.



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d| ε | = 1 everywhere demand price inelis u astnit ic.


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The demand curve is not linear. It is a rectangular hyperbola.



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The demand curve is not linear. It is a rectangular hyperbola.

The total revenue for each price-quantity combination remains the same.



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Along a linear downward-sloping demand curve, elasticity varies.

Objective 2: a linear downward-sloping demand curves and Objective 2: a linear downward-sloping demand curves and elasticityelasticity

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On the upper part of the demand curve, demand is price elastic.



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At the midpoint of the demand curve, demand is unit elastic.



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On the lower part of the demand curve, demand is price inelastic.




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On the lower part of the demand curve, demand is price inelastic.



The midpoint of a linear demand curve corresponds to the quantity that bisects the demand curve.


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Changes in price and quantity demanded result in changes in the total revenue received by firms.

Objective 3: …the relationship between the price elasticity of Objective 3: …the relationship between the price elasticity of demand and total revenue.demand and total revenue.

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Total Revenue = Price × Quantity Sold

Total Revenue = Total Expenditure


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Changes in total revenue are related to the price elasticity of demand.

Total Revenue = Price × Quantity Sold

Total Revenue = Total Expenditure


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If demand is price elasticelastic, %∆quantity demanded > %∆price.


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For example, if price rises by 10%, quantity demanded falls by more than 10%, say 12%.


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For example, if price rises by 10%, quantity demanded falls by more than 10%, say 12%. Therefore, total revenue must fall.

Price × Quantity Sold Total Revenue


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For example, if price rises by 10%, quantity demanded falls by more than 10%, say 12%. Therefore, total revenue must fall.


When demand is price elastic, changes in price and changes in total revenue move in opposite opposite directions.


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If demand is price inelastic,inelastic, %∆quantity demanded < %∆price.


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For example, if price rises by 10%, quantity demanded falls by less than 10%, say 8%.


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For example, if price rises by 10%, quantity demanded falls by less than 10%, say 8%. In this case, total revenue must rise.



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For example, if price rises by 10%, quantity demanded falls by less than 10%, say 8%. In this case, total revenue must rise.


When demand is price inelastic, changes in price and changes in total revenue move in the samesame direction.


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If demand is unit elasticunit elastic, %∆quantity demanded equals %∆price.


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For example, if price rises by 10%, quantity demanded falls by exactly 10%, resulting in no change in total revenue.


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For example, if price rises by 10%, quantity demanded falls by exactly 10%, resulting in no change in total revenue.

When demand is unit elastic, changes in price do not change total revenue. Total revenue is maximized.Total revenue is maximized.



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If demand is perfectly inelastic,perfectly inelastic, quantity demanded does not respond to changes in price but total revenue will changes when price changes.




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If demand is perfectly elastic,perfectly elastic, quantity demanded is infinitely responsive to changes in price.

Price × Quantity Sold to 0 Total Revenue to 0


module 8 price elasticity of demand 1. price elasticity of demand, define the price elasticity of...

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different elasticities