On the linear demand curve \( q = 40 - 2p \), at what price is the price elasticity of demand (absolute value) equal to 3?
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → 15
Given:
Demand curve: q = 40 − 2p, so a = 40 and b = 2
Required: |eD| = 3
On a linear demand curve q = a − bp, the price elasticity at price p is |eD| = bp / (a − bp).
\( \displaystyle \frac{2p}{40 - 2p} = 3 \)
2p = 120 − 6p
8p = 120, so p = 15
Check: q = 40 − 30 = 10, and |eD| = (2 × 15) / 10 = 3
The midpoint price a/2b = 10 gives elasticity 1. Elasticity is greater than 1 only above the midpoint, so the answer must be above Rs 10.
NCERT (2026-27): “2.6.1 Elasticity along a Linear Demand Curve Let us consider a linear demand curve q = a – bp. Note that at any point on the demand curve, the change in demand per unit change in the price ∆q/∆p = –b. … eD = –bp/(a – bp) (2.17) 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 ∞. 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. …” |