Consider the linear demand curve \( q = 30 - 3p \). Which of the following statements are correct?
(A) At a price of 0, the demand is 30 units.
(B) At a price of 8, the demand is inelastic.
(C) At a price of 5, the price elasticity of demand (absolute value) is 1.
(D) For a unit rise in price, the demand falls by 1/3 unit.
(E) At a price of 10, the demand is 0.
Choose the correct answer from the options given below:
Answer & explanation
Correct answer: option 4
The correct answer is Option (4) → (A), (C) and (E) only
For q = a − bp, here a = 30 and b = 3. Demand is a at zero price and zero at p = a/b = 10. Elasticity is 1 at the midpoint price a/2b = 5 and more than 1 above it.
(A) At a price of 0, the demand is 30 units. — Correct. q = 30 − 0 = 30.
(B) At a price of 8, the demand is inelastic. — Incorrect. 8 is above the midpoint price 5, so demand is elastic: |eD| = (3 × 8) / (30 − 24) = 4.
(C) At a price of 5, the price elasticity of demand (absolute value) is 1. — Correct. 5 = 30 / (2 × 3), the midpoint price.
(D) For a unit rise in price, the demand falls by 1/3 unit. — Incorrect. Demand falls by b = 3 units for each unit rise in price.
(E) At a price of 10, the demand is 0. — Correct. 30 − 3 × 10 = 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 … At p = a/2b, the elasticity is 1, at any price greater than 0 and less than a/2b, elasticity is less than 1, and at any price greater than a/2b, elasticity is greater than 1. …” |