For the linear demand curve \( d(p) = a - bp \), which of the following pairs is correctly matched?
Answer & explanation
Correct answer: option 4
The correct answer is Option (4) → \( a \) — Demand when the price is zero
Put p = 0 in d(p) = a − bp. Demand is then a. So a is the demand when the good is free.
Option (1) \( \displaystyle\frac{a}{b} \) — Fall in demand for a unit rise in price — demand becomes zero at the price a/b.
Option (2) \( \displaystyle\frac{a}{2b} \) — Price at which demand becomes zero — a/2b is the midpoint price, half of a/b.
Option (3) \( b \) — Price at which demand becomes zero — the number b is the fall in demand for a unit rise in price.
NCERT (2026-27): “Linear Demand … 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. Figure 2.15 depicts a linear demand curve.” |