Question

Suppose that the total revenue received by a company selling basketballs is \(\$ 600\) when the price is set at \(\$ 30\) per basketball and \(\$ 600\) when the price is set at \(\$ 20\) per basketball. Without using the midpoint formula, can you tell whether demand is elastic, inelastic, or unit-elastic over this price range?

Short answer

The demand is unit-elastic.

Step-by-step solution

Define elasticity concepts

Demand is elastic when a price change leads to a larger percentage change in quantity demanded, inelastic when the opposite is true, and unit-elastic when the percentage change in price and quantity demanded are equal.

Calculate quantity sold at different prices

At \\(30\ per basketball, total revenue of \\)600\ indicates \frac{600}{30} = 20\ balls were sold. At \\(20\ per basketball, total revenue of \\)600\ indicates \frac{600}{20} = 30\ balls were sold.

Analyze the revenue

Revenue remains constant at \\(600\ despite the price decrease from \\)30\ to \$20\. This suggests that the increase in quantity sold perfectly offsets the decrease in price.

Conclude elasticity by revenue analysis

Since total revenue remains constant despite a change in price, this indicates that the demand is unit-elastic over this price range. In unit-elastic demand, a change in price leads to a proportional change in quantity demanded, keeping revenue constant.

Key concepts

Price Elasticity of Demand

Price elasticity of demand measures how sensitive the demand for a good is to changes in its price. It helps us understand the relationship between price changes and consumer purchasing behavior. There are three primary categorizations:

• Elastic Demand: If a price change results in a more significant percentage change in quantity demanded, the demand is considered elastic. Consumers are highly responsive to price changes.
• Inelastic Demand: Here, a price change results in a smaller percentage change in the quantity demanded. Consumers are less responsive to changes in price.
• Unit-Elastic Demand: In this case, a change in price leads to an exactly proportional change in the quantity demanded. This means that the percentage change in price is equal to the percentage change in quantity demanded.

Price elasticity of demand can provide valuable insights for businesses as they plan pricing strategies and forecast revenue. In our exercise, the company's stable revenue despite a price change indicates unit-elastic demand because the proportional change in demand perfectly offsets the price change.

Elastic vs Inelastic Demand

Understanding whether demand is elastic or inelastic is crucial for businesses to set optimal pricing strategies.

• Elastic Demand: When the demand for a product is elastic, lowering the price can increase total revenue since the quantity demanded typically rises significantly. Conversely, increasing the price might sharply decrease total revenue because consumers will buy significantly less.
• Inelastic Demand: If demand is inelastic, consumers aren't as sensitive to price changes. So, even if prices increase, total revenue can still rise because consumers do not significantly reduce their purchases.

In our case, we see that a change from $30 to $20 price per basketball didn't change the total revenue, indicating that the demand was not elastic or inelastic but perfectly balanced as unit-elastic. This balance results in consistent revenue regardless of the price shift.

Revenue Analysis

Analyzing revenue is a straightforward method to identify demand elasticity. Total revenue is calculated as the product of price and quantity sold. By examining how total revenue responds to changes in price, businesses can infer the elasticity of demand:

• If total revenue increases with a price decrease, demand is elastic.
• If total revenue decreases with a price decrease, demand is inelastic.
• If total revenue remains unchanged with a price decrease, the demand is unit-elastic.

In the given exercise, the company experienced constant total revenue of $600 regardless of whether the price was $30 or $20. This stable revenue suggests unit-elastic demand, where changes in price and quantity demanded are exactly proportional to keep revenue steady. Understanding this relationship can help businesses optimize pricing and predict outcomes of different pricing strategies.