A unit elastic demand means that a price change leaves total revenue unchanged.

A unit elastic demand means that a price change leaves total revenue unchanged.

• A. True
• B. False
• C. Sometimes true
• D. Never true

Answer: (A)

Unit elastic demand means the percentage change in quantity demanded is exactly the opposite of the percentage change in price (the elasticity = 1 in magnitude). Because revenue is TR = P × Q, a tiny price change dP induces a quantity change dQ with dQ/Q = -dP/P. The change in revenue is dTR = P dQ + Q dP, and substituting dQ = -(Q/P) dP gives dTR = 0. So, for small price changes, total revenue stays the same when demand is unit elastic. Note that for larger, finite price changes the result isn’t guaranteed to be exact, since elasticity may vary along the curve, but at the unit-elastic point the revenue is locally flat (maximizes revenue in the broader sense).

Unit elastic demand means the percentage change in quantity demanded is exactly the opposite of the percentage change in price (the elasticity = 1 in magnitude). Because revenue is TR = P × Q, a tiny price change dP induces a quantity change dQ with dQ/Q = -dP/P. The change in revenue is dTR = P dQ + Q dP, and substituting dQ = -(Q/P) dP gives dTR = 0. So, for small price changes, total revenue stays the same when demand is unit elastic. Note that for larger, finite price changes the result isn’t guaranteed to be exact, since elasticity may vary along the curve, but at the unit-elastic point the revenue is locally flat (maximizes revenue in the broader sense).