On a linear demand curve, elasticity is higher at higher prices than at lower prices.

• A. True
• B. False
• C. Constant along the curve.
• D. Elasticity is independent of price.

Answer: (A)

The key idea is that elasticity depends on the ratio P to Q, not just the slope of the demand line. For a linear downward-sloping demand, you can write Q as a function of P with a constant slope: dQ/dP is a constant negative number. Price elasticity of demand is ε = (dQ/dP) × (P/Q). Since dQ/dP is fixed, elasticity changes only because the ratio P/Q changes as you move along the curve.

As price rises and quantity falls, the ratio P/Q grows in absolute value. Near the high-price end of the curve, price is large and quantity is small, so P/Q is large and the magnitude of ε is large. Near the low-price end, price is small and quantity is large, so P/Q is small and ε is small. This means elasticity is not constant along a linear demand curve; it increases in magnitude as you move to higher prices.

So the statement that elasticity is higher at higher prices than at lower prices is true.