1. Price Elasticity of Demand
Module 8
Price Elasticity of Demand

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

3. Objective 1: Define the price elasticity of demand, understand why it is useful….
The price elasticity of demand measures the responsiveness of the quantity demanded to changes
in price.
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.

4. Objective 1: ….how to calculate the price elasticity of demand
All elasticity formulas may be stated as fractions or ratios of two percentage change values.
The formula for the price elasticity of demand is:

5. Objective 1: ….how to calculate the price elasticity of demand
Note:
The elasticity formula always 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 values of the price elasticity of demand and so that the negative sign is ignored. 5

6. Objective 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?
Solving the Problem
Apply the elasticity formula:

7. %∆ in Quantity Demanded = |Price Elasticity of Demand| x %∆Price
Objective 1: calculating the price elasticity of demand
The price elasticity of demand = 2. What does the number 2 mean?
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
For every 1 percent increase in price, quantity demanded falls by 2 percent, or for every 1 percent decreases in price, quantity demanded increases by 2 percent. 7

8. Objective 1: calculating the price elasticity of demand
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.
Solving the Problem
Essentially, we are given two
price-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
midpoint formula.

9. Objective 1: ..the mid-point formula
Simplify by cancelling the ½s and the 100s to give: 9

10. Objective 1: ..the mid-point formula
Now plug in the given values:
The average elasticity between a and b is 0.75 

11. Understand how to describe elasticities,….
Objective 2
Understand how to describe elasticities,….
When demand is price elastic, the change in quantity demanded is proportionally greater than the change in price.

12. Objective 2: describing elasticities,….
When demand is price inelastic, the change in quantity demanded is proportionally smaller than the change in price. 12

13. Objective 2: describing elasticities,….
When demand is unit price elastic, the change in quantity demanded is equal to the change in price. 13

14. Objective 2: describing elasticities,….
The polar cases:
Perfectly inelastic demand occurs when a change in price results in no change in quantity demanded. 14

15. Objective 2: describing elasticities,….
The polar cases:
Perfectly elastic demand occurs when a change in price results in an infinite change in quantity demanded.

16. Objective 2: graph demand curves to represent different elasticities…
Quantity demanded does not respond to changes in price. Examples include some types of medication such as insulin for a diabetic.

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

18. Objective 2: graph demand curves to represent different elasticities…
The demand curve is not linear. It is a rectangular hyperbola.
The total revenue for each price-quantity combination remains the same.

19. Objective 2: a linear downward-sloping demand curves and elasticity
Along a linear downward-sloping demand curve,
elasticity varies.
On the upper part of the demand
curve, demand is price elastic.
The midpoint of a linear demand curve corresponds to the quantity that bisects the demand curve.
At the midpoint of the demand curve, demand is unit elastic.
On the lower part of the demand
curve, demand is price inelastic.

20. Total Revenue = Price × Quantity Sold
Objective 3: …the relationship between the price elasticity of demand and total revenue.
Changes in price and quantity demanded result in changes in the total revenue received by firms.
Changes in total revenue are related to the price
elasticity of demand.
Total Revenue = Price × Quantity Sold
Total Revenue = Total Expenditure

21. Price  × Quantity Sold   Total Revenue 
Objective 3: …the relationship between the price elasticity of demand and total revenue.
If demand is price elastic, %∆quantity demanded > %∆price.
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 
When demand is price elastic, changes in price and changes in total revenue move in opposite directions. 21

22. Price  × Quantity Sold   Total Revenue 
Objective 3: …the relationship between the price elasticity of demand and total revenue.
If demand is price inelastic, %∆quantity demanded < %∆price.
For example, if price rises by 10%, quantity demanded falls by less than 10%, say 8%. In this case, total revenue must rise.
Price  × Quantity Sold   Total Revenue 
When demand is price inelastic, changes in price and changes in total revenue move in the same direction.

23. Price  × Quantity Sold   Total Revenue 
Objective 3: …the relationship between the price elasticity of demand and total revenue.
If demand is unit elastic, %∆quantity demanded equals %∆price.
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.
Price  × Quantity Sold   Total Revenue 

24. Objective 3: …the relationship between the price elasticity of demand and total revenue.
If demand is perfectly inelastic, quantity demanded does not respond to changes in price but total revenue will changes when price changes.
Price  × Quantity Sold   Total Revenue 
Price  × Quantity Sold   Total Revenue 

25. Objective 3: …the relationship between the price elasticity of demand and total revenue.
If demand is perfectly elastic, quantity demanded is infinitely responsive to changes in price.
Price  × Quantity Sold  to 0  Total Revenue  to 0