Moving up along a linear demand curve, the price elasticity of demand

Moving up along a linear demand curve, the price elasticity of demand

• A. at first increases and then decreases.
• B. increases.
• C. decreases.
• D. does not change.

Answer: (B)

The key idea is how elasticity behaves when you move along a linear downward-sloping demand curve. Elasticity measures the percent change in quantity for a percent change in price, and on a straight-line demand the slope is constant but the ratio of price to quantity changes as you move. If the demand is Q = a − bP, then elasticity E = (dQ/dP) × (P/Q) = (−b) × (P/(a − bP)) = −bP/(a − bP). As price P increases along the curve, the numerator grows while the denominator shrinks, so the magnitude |E| rises. Near low prices (where Q is large), elasticity is small (inelastic); as price climbs toward the intercept (where Q → 0), elasticity becomes very large (elastic). Therefore moving up along a linear demand curve makes the price elasticity of demand increase.

The key idea is how elasticity behaves when you move along a linear downward-sloping demand curve. Elasticity measures the percent change in quantity for a percent change in price, and on a straight-line demand the slope is constant but the ratio of price to quantity changes as you move.

If the demand is Q = a − bP, then elasticity E = (dQ/dP) × (P/Q) = (−b) × (P/(a − bP)) = −bP/(a − bP). As price P increases along the curve, the numerator grows while the denominator shrinks, so the magnitude |E| rises. Near low prices (where Q is large), elasticity is small (inelastic); as price climbs toward the intercept (where Q → 0), elasticity becomes very large (elastic). Therefore moving up along a linear demand curve makes the price elasticity of demand increase.