On a straight-line downward-sloping demand curve with an intercept of 100 units, the elasticity at the midpoint (50 units) is:

On a straight-line downward-sloping demand curve with an intercept of 100 units, the elasticity at the midpoint (50 units) is:

• A. Greater than 1
• B. 1.0
• C. 0.5
• D. 0

Answer: (B)

Elasticity varies along a linear downward-sloping demand curve, and at the midpoint of the quantity range the magnitude of elasticity is 1. Here, with a quantity intercept of 100, the midpoint is 50. If the demand line is written as Q = 100 − bP, then the slope is dQ/dP = −b. The elasticity is ε = (dQ/dP) × (P/Q) = (−b) × (P/Q). At Q = 50, P = 50/b, so ε = (−b) × ( (50/b) / 50 ) = −1. The magnitude is 1, i.e., unit elastic. Therefore the correct interpretation is 1.0. The other values would imply elasticity above, below, or equal to zero, which doesn’t occur at this midpoint.

Elasticity varies along a linear downward-sloping demand curve, and at the midpoint of the quantity range the magnitude of elasticity is 1. Here, with a quantity intercept of 100, the midpoint is 50. If the demand line is written as Q = 100 − bP, then the slope is dQ/dP = −b. The elasticity is ε = (dQ/dP) × (P/Q) = (−b) × (P/Q). At Q = 50, P = 50/b, so ε = (−b) × ( (50/b) / 50 ) = −1. The magnitude is 1, i.e., unit elastic. Therefore the correct interpretation is 1.0. The other values would imply elasticity above, below, or equal to zero, which doesn’t occur at this midpoint.