For the linear demand curve \( d(p) = a - bp \), which of the following statements is NOT correct?
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → The price elasticity of demand is the same at every point on it.
On a straight-line demand curve the slope is the same everywhere, but the elasticity changes from point to point.
Option (1) The demand falls by b units for each unit rise in price. — True. The slope is −b.
Option (2) The price elasticity of demand is the same at every point on it. — False. Elasticity is 0 where the curve meets the quantity axis, 1 at the midpoint and very large near the price axis. It differs at different points.
Option (3) At a price of 0, the demand is a. — True. Put p = 0: d(0) = a.
Option (4) At a price of \( \displaystyle\frac{a}{b} \), the demand is 0. — True. Put p = a/b: a − b(a/b) = 0.
NCERT (2026-27): “Linear Demand A linear demand curve can be written as d(p) = a – bp; … where a is the vertical intercept, –b is the slope of the demand curve. At price 0, the demand is a, and at price equal to a/b, the demand is 0. The slope of the demand curve measures the rate at which demand changes with respect to its price. For a unit increase in the price of the good, the demand falls by b units. …” “2.6.1 Elasticity along a Linear Demand Curve … From (2.17), it is clear that the elasticity of demand is different at different points on a linear demand curve. At p = 0, the elasticity is 0, at q = 0, elasticity is ∞. …” |