If a 4 percent rise in the price of peanut butter lowers the total revenue by 4 percent, the demand for peanut butter is

If a 4 percent rise in the price of peanut butter lowers the total revenue by 4 percent, the demand for peanut butter is

• A. inelastic
• B. elastic
• C. elasticity greater than 1.
• D. unit elastic

Answer: (D)

The key idea is how total revenue responds to a price change, which depends on the price elasticity of demand. If raising price lowers revenue, demand is elastic (the percentage drop in quantity demanded is larger than the percentage rise in price). Here, price goes up 4% and total revenue falls 4%. Using the small-change approximation, %ΔR ≈ %ΔP + %ΔQ. So -4% ≈ +4% + %ΔQ, which gives %ΔQ ≈ -8%. The elasticity of demand is the ratio of the percentage change in quantity to the percentage change in price: |%ΔQ| / |%ΔP| ≈ 8% / 4% = 2. Since this magnitude is greater than 1, the demand is elastic. Even with a precise calculation, (1 + 0.04)(1 + %ΔQ) = 1 - 0.04 leads to %ΔQ ≈ -7.69%, giving elasticity ≈ (-7.69%)/(4%) ≈ -1.92, still elastic. So the situation indicates elastic demand.

The key idea is how total revenue responds to a price change, which depends on the price elasticity of demand. If raising price lowers revenue, demand is elastic (the percentage drop in quantity demanded is larger than the percentage rise in price).

Here, price goes up 4% and total revenue falls 4%. Using the small-change approximation, %ΔR ≈ %ΔP + %ΔQ. So -4% ≈ +4% + %ΔQ, which gives %ΔQ ≈ -8%. The elasticity of demand is the ratio of the percentage change in quantity to the percentage change in price: |%ΔQ| / |%ΔP| ≈ 8% / 4% = 2. Since this magnitude is greater than 1, the demand is elastic.

Even with a precise calculation, (1 + 0.04)(1 + %ΔQ) = 1 - 0.04 leads to %ΔQ ≈ -7.69%, giving elasticity ≈ (-7.69%)/(4%) ≈ -1.92, still elastic. So the situation indicates elastic demand.