1. Price Elasticity and Total Revenue

2. Price Elasticity and Total Revenue
The importance of price elasticity of demand for firms relates to the effect of price changes on total revenue and thus on profits.
Recall, Total Revenue = Price x Quantity
Elastic Demand and Total Revenue: if demand is elastic, an increase (a decrease) in price causes a decrease (an increase) in total revenue
If the demand is elastic, a price change causes total revenue to change in the opposite direction

3. Revenue Changes with Elastic Demand
Example; Demand curve for Videos
Suppose that the original price is $5 and the original quantity demanded is 500 videos
Thus, the original total revenue is TR = P x Q = $5 x 500 = $2, 500
This is represented by the areas A + B
Now, if the price is decreased from $5 to $3 (i.e. decreased by 40 %) the quantity increases from 500 to 1500 videos (i.e. increased by 200%)
That is, the demand for videos is elastic and the total revenue is given by
TR = P x Q = $3 x $1500 = $4, 600
This is represented by areas B + C

4. Hence, when the demand is elastic, a decrease in price causes an increase in TR.

5. In general for elastic demand,
Price Rises: TR falls, rectangle B is gained, rectangle C is lost
Price Falls: TR rises, rectangle B is lost, rectangle C is gained

6. Revenue Changes with Inelastic Demand
Inelastic Demand and Total Revenue: if the demand is inelastic, and increase (a decrease) in price cause an increase (a decrease) in the total revenue
If the demand is inelastic, a price change causes total revenue to change in the same direction
Example; Demand curve for Amusement Park Rides
Suppose that the original price is $2 and the original quantity demanded is 10,000 riders
Thus, the original total revenue is TR = P x Q = $2 x = $20 000
This is represented by area F + G

7. Now, if the price is increased from $2 to $3 (i. e
Now, if the price is increased from $2 to $3 (i.e. increased by 50%), the quantity demanded will decrease from 10,000 to 8,000 riders (i.e. decreased by 20%)
That is, the demand for videos is inelastic and the total revenue is
TR = P x Q = $3 x = $24 000
This is represented by areas E + F
Hence, when the demand is inelastic, a increase in price causes an increase in TR

8. In general for inelastic demand,
Price rises: TR rises, Rectangle E is gained, Rectangle G is lost
Price fall: TR falls, Rectangle E is lost, Rectangle G is gained

9. Revenue Change with Unit-Elastic Demand
Unitary-Demand and Total Revenue: if the demand is unit-elastic, a change in price will not change the total revenue
Example; Demand for Videos
Suppose that the original price is $3 and the original quantity demanded is 1,000 videos.
Thus, the original total revenue is TR = P x Q = $3 x 1000 = $3 000
This is represented by area I + J
Now, if the price is increased from $3 to $6 (i.e. increased by 100%) then quantity demanded will decrease from 1,000 to 500 videos (i.e. decreased by 100%)

10. That is, the demand for videos is elastic and total revenue is,
TR = P x Q = $6 x 500 = $3, 000
This is represented by the area H + I
Hence, when the demand is unit-elastic, a change in price will not change the TR
Area H = Area J

11. Change in Total Revenue
Summary
Total revenue and price elasticity of demand can be summarized in the following table:
Price Change
Change in Total Revenue
Change in Quantity
Elastic Demand (|ED| >1) Up
Down
Decrease (More than proportionally)
Increase (More than proportionally)
Unitary Elasticity (|ED| = 1)
Unchanged
Decrease (Proportionate)
Increase (Proportionate)
Inelastic Demand (|ED| <1)
Decrease (Less than proportionate)
Increase (More than proportionate)

12. Elasticity on a Linear Demand Curve
Elasticity typically changes at every point along the same demand curve; for all straight-lines and most other demand curves
Demand is more elastic toward the upper left
At high prices the average price is relatively large and the change in the average quantity demanded is relatively small
Demand is less elastic toward the lower right
At low prices the average price is relatively small and the average quantity demanded is relatively large

13. Example; Price elasticity of demand for movie tickets

14. Graphically we can illustrate both the price elasticity and total revenue,