For a linear demand curve, elasticity tends to be higher at higher prices and lower at lower prices.

For a linear demand curve, elasticity tends to be higher at higher prices and lower at lower prices.

• A. Elasticity is constant.
• B. Elasticity is infinite near the origin.
• C. Elasticity tends to be higher at higher prices and lower at lower prices.
• D. Elasticity does not depend on price.

Answer: (C)

The key idea is that elasticity varies along a linear demand curve. For a downward-sloping line, the price elasticity of demand is not constant; its magnitude rises as price rises. If the demand is Q = a − bP, then dQ/dP = −b and ε = (dQ/dP) × (P/Q) = −b × [P/(a − bP)]. As price increases, the ratio P/(a − bP) grows, so the magnitude of ε increases. At very low prices (P near 0), Q is near a and ε is near 0, meaning demand is inelastic in that range. As price approaches the choke price (where Q → 0), ε grows without bound in magnitude. This shows elasticity tends to be higher at higher prices and lower at lower prices. The other statements conflict with this behavior: elasticity is not constant, it is not infinite near the origin, and it does depend on price.

The key idea is that elasticity varies along a linear demand curve. For a downward-sloping line, the price elasticity of demand is not constant; its magnitude rises as price rises.

If the demand is Q = a − bP, then dQ/dP = −b and ε = (dQ/dP) × (P/Q) = −b × [P/(a − bP)]. As price increases, the ratio P/(a − bP) grows, so the magnitude of ε increases. At very low prices (P near 0), Q is near a and ε is near 0, meaning demand is inelastic in that range. As price approaches the choke price (where Q → 0), ε grows without bound in magnitude. This shows elasticity tends to be higher at higher prices and lower at lower prices. The other statements conflict with this behavior: elasticity is not constant, it is not infinite near the origin, and it does depend on price.