Total Revenue and Elasticity

Total Revenue and Elasticity

Understanding Total Revenue

Total revenue is the total amount of money received from the sale of a good, calculated as the price of the good multiplied by the quantity sold.

• Formula: $\text{Total Revenue (TR)} = \text{Price (P)} \times \text{Quantity (Q)}$

• When the price of a good changes, total revenue also changes, but not always in a straightforward way.

Elasticity of Demand and Its Effect on Total Revenue

The effect of a price change on total revenue depends on the price elasticity of demand:

• Elastic Demand: A 1% price cut increases the quantity sold by more than 1%, causing total revenue to increase.

• Inelastic Demand: A 1% price cut increases the quantity sold by less than 1%, causing total revenue to decrease.

• Unit Elastic Demand: A 1% price cut increases the quantity sold by exactly 1%, so total revenue does not change.

Graphical Representation

Figure 4.5 illustrates the relationship between elasticity and total revenue using the example of pizza sales:

• At high prices (e.g., $25), demand is elastic. Lowering the price increases total revenue.

• At low prices (e.g., below $12.50), demand is inelastic. Lowering the price decreases total revenue.

• At the midpoint price ($12.50), demand is unit elastic, and total revenue is maximized.

Price Range	Elasticity	Effect of Price Cut on Total Revenue
$25 to $12.50	Elastic	Increases
$12.50 to $0	Inelastic	Decreases
At $12.50	Unit Elastic	No Change (Maximum TR)

Total Revenue Test

The total revenue test is a practical method for estimating the price elasticity of demand by observing how total revenue changes as price changes (holding all other factors constant):

• 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.

Example Application

• Suppose the price of pizza drops from $25 to $12.50. If total revenue rises, demand is elastic in this range.

• If the price drops further from $12.50 to $0 and total revenue falls, demand is inelastic in this range.

• At $12.50, total revenue is at its maximum, indicating unit elasticity.

Summary Table: Elasticity and Total Revenue

Elasticity	Effect of Price Cut on TR	Effect of Price Increase on TR
Elastic	Increases	Decreases
Inelastic	Decreases	Increases
Unit Elastic	No Change	No Change

Key Formula:

$\text{Total Revenue} = \text{Price} \times \text{Quantity}$

Additional info: The total revenue test is a foundational tool in microeconomics for analyzing consumer behavior and market outcomes, especially when direct calculation of elasticity is difficult.