Refer to the accompanying table. The price elasticity of demand of erasers is $\qquad$ when the price is lowered from $1.50 to $1.00. Sellers of erasers will $\qquad$ their total revenue from this price change.
| Price of Erasers | Quantity Demanded of Erasers | Quantity Demanded of Pencils |
|---|---|---|
| $0.50 | 10 | 12 |
| $1.00 | 8 | 11 |
| $1.50 | 7 | 10 |
| $2.00 | 6 | 9 |
| $2.50 | 5 | 8 |
A. elastic; lower
B. perfectly elastic; not change
C. inelastic; lower
D. elastic; raise
E. inelastic; raise
Answer (2)
Calculate the percentage change in quantity demanded: 7 8 − 7 × 100 ≈ 14.29% .
Calculate the percentage change in price: $1.50 $1.00 − $1.50 × 100 ≈ − 33.33% .
Calculate the price elasticity of demand: − 33.33% 14.29% ≈ − 0.43 . Since ∣ − 0.43∣ < 1 , demand is inelastic.
Calculate total revenue at both prices: Original revenue = $1.50 × 7 = $10.50 , New revenue = $1.00 × 8 = $8.00 . Total revenue decreases, so the answer is inelastic; lower.
Explanation
Understanding the Problem We are given a table with the price of erasers and the corresponding quantity demanded. We want to find the price elasticity of demand when the price is lowered from $1.50 to $1.00, and determine whether the sellers' total revenue will increase or decrease as a result of this price change.
Calculating Percentage Changes First, we need to calculate the percentage change in quantity demanded and the percentage change in price.
Percentage Change in Quantity Demanded The percentage change in quantity demanded is calculated as: Old Quantity New Quantity − Old Quantity × 100 = 7 8 − 7 × 100 = 7 1 × 100 ≈ 14.29%
Percentage Change in Price The percentage change in price is calculated as: Old Price New Price − Old Price × 100 = $1.50 $1.00 − $1.50 × 100 = $1.50 − $0.50 × 100 = − 3 1 × 100 ≈ − 33.33%
Calculating Price Elasticity of Demand Next, we calculate the price elasticity of demand, which is the percentage change in quantity demanded divided by the percentage change in price: Price Elasticity of Demand = % Change in Price % Change in Quantity = − 33.33% 14.29% ≈ − 0.43
Determining Elasticity The absolute value of the price elasticity of demand is ∣ − 0.43∣ = 0.43 . Since this value is less than 1, the demand is inelastic.
Calculating Total Revenue Now, we calculate the total revenue at the original price and the new price. Total revenue is calculated as Price × Quantity.
Original and New Total Revenue The original total revenue is: $1.50 × 7 = $10.50 The new total revenue is: $1.00 × 8 = $8.00
Impact on Total Revenue Since the total revenue decreased from $10.50 to $8.00 , sellers will lower their total revenue from this price change.
Final Answer Therefore, the price elasticity of demand is inelastic, and sellers of erasers will lower their total revenue from this price change.
Examples
Understanding price elasticity of demand is crucial for businesses. For example, a movie theater might consider lowering ticket prices to attract more customers. If the demand for movie tickets is inelastic (less than 1), lowering prices will decrease total revenue, meaning fewer profits. However, if the demand is elastic (greater than 1), lowering prices will increase total revenue, leading to higher profits. This concept helps businesses make informed decisions about pricing strategies to maximize their revenue.
The price elasticity of demand for erasers when the price is lowered from $1.50 to $1.00 is inelastic, and as a result, sellers will lower their total revenue due to this price change. Therefore, the correct option is E: inelastic; lower.
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