Which statement about a straight-line demand curve is true?

Which statement about a straight-line demand curve is true?

• A. The elasticity is zero at all prices.
• B. The elasticity is the same at all prices.
• C. The elasticity differs across prices.
• D. The demand is perfectly elastic at all prices.

Answer: (C)

A straight-line downward-sloping demand curve has a constant slope, but price elasticity of demand varies along the curve because elasticity depends on the ratio of price to quantity (ε = (dQ/dP) × (P/Q)). For a linear demand, Q = a − bP, the slope dQ/dP = −b is constant, so elasticity becomes ε = −b × P/(a − bP). As P changes, the ratio P/(a − bP) changes, causing ε to move from inelastic at low prices (small P relative to Q) to elastic at high prices (large P relative to Q). There is a point where it’s unit elastic (ε = −1), typically somewhere near the midpoint of the curve. Because elasticity isn’t constant across the price range, the statement that elasticity differs across prices is true. The other statements fail because elasticity is not zero at all prices, not the same at all prices, and the demand is not perfectly elastic at all prices.

A straight-line downward-sloping demand curve has a constant slope, but price elasticity of demand varies along the curve because elasticity depends on the ratio of price to quantity (ε = (dQ/dP) × (P/Q)). For a linear demand, Q = a − bP, the slope dQ/dP = −b is constant, so elasticity becomes ε = −b × P/(a − bP). As P changes, the ratio P/(a − bP) changes, causing ε to move from inelastic at low prices (small P relative to Q) to elastic at high prices (large P relative to Q). There is a point where it’s unit elastic (ε = −1), typically somewhere near the midpoint of the curve. Because elasticity isn’t constant across the price range, the statement that elasticity differs across prices is true. The other statements fail because elasticity is not zero at all prices, not the same at all prices, and the demand is not perfectly elastic at all prices.