A consumer’s demand curve is \( pq = 120 \), where p is the price and q the quantity. Which of the following statements are correct?
(A) Her expenditure on the good is Rs 120 at every price.
(B) The curve is a straight line, with elasticity 1 only at its midpoint.
(C) The price elasticity of demand (absolute value) is 1 at every point on the curve.
(D) At a price of Rs 6, she buys 20 units.
(E) At a price of Rs 8, she buys 16 units.
Choose the correct answer from the options given below:
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → (A), (C) and (D) only
A demand curve of the form pq = constant is a rectangular hyperbola. Price × quantity, which is expenditure, is the same at every point, and elasticity is 1 everywhere.
(A) Her expenditure on the good is Rs 120 at every price. — Correct. Expenditure = pq = 120.
(B) The curve is a straight line, with elasticity 1 only at its midpoint. — Incorrect. pq = 120 is a downward sloping curve, and its elasticity is 1 at every point.
(C) The price elasticity of demand (absolute value) is 1 at every point on the curve. — Correct. A percentage change in price brings an equal percentage change in quantity.
(D) At a price of Rs 6, she buys 20 units. — Correct. q = 120 / 6 = 20.
(E) At a price of Rs 8, she buys 16 units. — Incorrect. q = 120 / 8 = 15.
NCERT (2026-27): “Rectangular Hyperbola An equation of the form xy = c where x and y are two variables and c is a constant, giving us a curve called rectangular hyperbola. It is a downward sloping curve in the x-y plane as shown in the diagram. … If the equation of a demand curve takes the form pq = e, where e is a constant, it will be a rectangular hyperbola, where price (p) times quantity (q) is a constant. With such a demand curve, no matter at what point the consumer consumes, her expenditures are always the same and equal to e.” “Constant Elasticity Demand Curve … Figure 2.20(c) depicts a demand curve which has the shape of a rectangular hyperbola. This demand curve has a property that a percentage change in price along the demand curve always leads to equal percentage change in quantity. Therefore, |eD| = 1 at every point on this demand curve. This demand curve is called the unitary elastic demand curve.” |