Question

suppose that over one range of prices, the absolute value of the price elasticity of demand varies from 15.0 to 2.5, and over another range of prices, the absolute value of the price elasticity of demand varies from 1.5 to 0.75. what can you say about total revenue and the total revenue curve over these two ranges of the demand curve as price falls? a. in the first case total revenue rises and in the second case total revenue rises. b. in the first case total revenue rises and in the second case total revenue rises and then falls. c. in the first case total revenue falls and in the second case total revenue falls. d. in the first case total revenue falls and in the second case total revenue falls and then rises. e. there is insufficient information to determine the effect on total revenue.

Explanation:

To solve this, we use the relationship between price elasticity of demand (PED) and total revenue (TR):

• When \( |\text{PED}| > 1 \) (elastic demand), a price decrease leads to an increase in TR (because the percentage increase in quantity demanded is greater than the percentage decrease in price).
• When \( |\text{PED}| < 1 \) (inelastic demand), a price decrease leads to a decrease in TR (because the percentage increase in quantity demanded is less than the percentage decrease in price).

Analyzing the two ranges:

1. First range: \( |\text{PED}| \) varies from 15.0 to 2.5. Both values are \( > 1 \) (elastic demand). So, when price falls, TR rises.
2. Second range: \( |\text{PED}| \) varies from 1.5 to 0.75. Here, 1.5 \( > 1 \) (elastic, TR rises) and 0.75 \( < 1 \) (inelastic, TR falls). Thus, as price falls, TR first rises (when \( |\text{PED}| > 1 \)) and then falls (when \( |\text{PED}| < 1 \)).

This matches option B: "In the first case total revenue rises and in the second case total revenue rises and then falls."

Answer:

B. In the first case total revenue rises and in the second case total revenue rises and then falls.