A student asks…
What is the total revenue test of the price elasticity of demand? Does it work for the demand for all goods?
The short answers is “a test of the price elasticity of demand using a change in total revenue” and “yes.”
How does total revenue depend on the price and the quantity sold?
The total revenue from the sale of a good equals the product of the price of the good and the quantity sold. A ceteris paribus increase in the price or the quantity sold increases the total revenue. But the law of demand guarantees an inverse relationship between the price and the quantity sold, so an increase in either variable brings a change to total revenue that is not ceteris paribus.
What is the price elasticity of demand?
The definition of the price elasticity of demand is
Demand is elastic if the price elasticity of demand is greater than 1. Demand is inelastic if the price elasticity of demand is less than 1. And demand is unit elastic if the price elasticity of demand is equal to 1.
What is the total revenue test?
Because cutting the price brings an increase in the quantity sold, a price cut might increase, decrease, or not change the total revenue. The total revenue test is a method of estimating the price elasticity of demand by observing the change in total revenue that results from a change in the price, when all other influences on the quantity sold remain the same.
- If a price cut increases total revenue, demand is elastic.
- If a price cut decreases total revenue, demand is inelastic.
- If a price cut leaves total revenue unchanged, demand is unit elastic.
Why does the total revenue test work?
When the price is cut, the quantity sold increases. Whether total revenue increases depends on the percentage changes of the two variables. In percentage terms, if the quantity change exceeds the price change, total revenue increases; if the price change exceeds the quantity change, total revenue decreases; and if the changes are equal, total revenue remains the same.
Because the price elasticity of demand and the change in total revenue both depend on these percentage changes, there is a direct connection between the price elasticity of demand and the change in total revenue. If total revenue increases, demand is elastic because the price change exceeds the quantity change; if total revenue decreases, demand is inelastic because the quantity change exceeds the price change; and if total revenue remains the same, demand is unit elastic because the changes are equal. Table 1 summarizes this connection.
How does the total revenue test work on a graph?
Figure 1 shows the relationship between a demand curve and total revenue.
Moving down along the demand curve in part (a), the price elasticity of demand decreases. Demand is elastic when the quantity demanded (and sold) is less than 25 pizzas an hour. Demand is unit elastic when the quantity demand is 25 pizzas an hour. And demand is inelastic when the quantity demanded is greater than 25 pizzas an hour.
Part (b) shows the total revenue for the same quantities. When demand is elastic (i.e., the quantity demanded is less than 25 pizzas an hour), a price cut increases total revenue. When demand is unit elastic (i.e., the quantity demanded is 25 pizzas an hour), a price cut leaves total revenue unchanged. And when demand is elastic (i.e., the quantity demanded is greater than 25 pizzas an hour), a price cut decreases total revenue.
Must the demand curve be linear for the total revenue test to work?
For the total revenue test to work, demand need only slope downward. A downward-sloping linear demand curve satisfies this condition and so do other downward-sloping demand curves. If the price and the quantity demanded have an inverse relationship, the total revenue test works.
What happens when the price elasticity of demand is constant?
The total revenue test works when the price elasticity of demand is constant. The video below answers this question in more detail.
You can explore the demand and total revenue graphs here.
Work these questions to solidify your understanding of the lesson and get instant feedback.