A straight-line demand curve with negative slope intersects the horizontal axis at 200 units. The point where elasticity equals 1 corresponds to a quantity of

A straight-line demand curve with negative slope intersects the horizontal axis at 200 units. The point where elasticity equals 1 corresponds to a quantity of

• A. A negative quantity would occur.
• B. 100 units.
• C. 0 units.
• D. 200 units.

Answer: (B)

Elasticity along a linear demand curve varies with where you are on the line. If the quantity demanded depends linearly on price with Q = 200 − bP (b > 0), then the price elasticity of demand is E = (dQ/dP)·(P/Q) = (−b)·(P/Q) = −bP/Q. The point where elasticity equals 1 in magnitude satisfies |E| = 1, so −bP/Q = −1 or Q = bP. Using Q = 200 − bP, substitute Q = bP to get bP = 200 − bP, which gives 2bP = 200, hence Q = bP = 100. Therefore, the quantity where elasticity equals 1 is 100 units.

Elasticity along a linear demand curve varies with where you are on the line. If the quantity demanded depends linearly on price with Q = 200 − bP (b > 0), then the price elasticity of demand is E = (dQ/dP)·(P/Q) = (−b)·(P/Q) = −bP/Q. The point where elasticity equals 1 in magnitude satisfies |E| = 1, so −bP/Q = −1 or Q = bP.

Using Q = 200 − bP, substitute Q = bP to get bP = 200 − bP, which gives 2bP = 200, hence Q = bP = 100. Therefore, the quantity where elasticity equals 1 is 100 units.