Price Elasticity and Total Revenue

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

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

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

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

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 10 000 = $20 000 This is represented by area F + G

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 8 000 = $24 000 This is represented by areas E + F Hence, when the demand is inelastic, a increase in price causes an increase in TR

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

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%)

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

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)

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

Example; Price elasticity of demand for movie tickets

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