On a linear demand curve that intersects both axes, which statement is true about elasticity as price falls and quantity increases?

On a linear demand curve that intersects both axes, which statement is true about elasticity as price falls and quantity increases?

• A. Elasticity decreases.
• B. Elasticity is less than 1 at all prices.
• C. Elasticity equals 1 at all prices.
• D. Elasticity exceeds 1 at all prices.

Answer: (A)

On a linear demand curve, elasticity is not constant; it changes as you move along the curve because it depends on the ratio of price to quantity. For a line with P = a − bQ, the elasticity of demand is Ed = (dQ/dP) × (P/Q. Since dQ/dP = −1/b, this becomes Ed = −P/(a − P). The magnitude is |Ed| = P/(a − P). As price falls (P decreases) and quantity rises (Q increases), the denominator (a − P) grows while the numerator P shrinks, so |Ed| decreases. Near the top of the curve (high price, low quantity) elasticity is large, and near the bottom (low price, high quantity) elasticity is small. That’s why the statement that elasticity decreases as price falls and quantity increases is the best answer. Elasticity being less than 1 at all prices, equal to 1 at all prices, or greater than 1 at all prices would not hold on a linear demand curve, since elasticity changes with position on the curve.

On a linear demand curve, elasticity is not constant; it changes as you move along the curve because it depends on the ratio of price to quantity. For a line with P = a − bQ, the elasticity of demand is Ed = (dQ/dP) × (P/Q. Since dQ/dP = −1/b, this becomes Ed = −P/(a − P). The magnitude is |Ed| = P/(a − P).

As price falls (P decreases) and quantity rises (Q increases), the denominator (a − P) grows while the numerator P shrinks, so |Ed| decreases. Near the top of the curve (high price, low quantity) elasticity is large, and near the bottom (low price, high quantity) elasticity is small.

That’s why the statement that elasticity decreases as price falls and quantity increases is the best answer. Elasticity being less than 1 at all prices, equal to 1 at all prices, or greater than 1 at all prices would not hold on a linear demand curve, since elasticity changes with position on the curve.