The demand for a normal good is q = 100 - 4p. A rise in income changes it to q = 120 - 4p. What is the price elasticity of demand (in absolute value) at a price of Rs 15, before and after the rise in income?
Answer & explanation
Correct answer: option 1
The correct answer is Option (1) → 1.5 before and 1 after
On a linear demand curve q = a − bp, the elasticity is eD = −bp/(a − bp). The rise in income shifts the demand curve of this normal good to the right, from a = 100 to a = 120.
Given:
Before: q = 100 − 4p
After: q = 120 − 4p
Price = Rs 15
Before the rise in income:
\( \displaystyle q = 100 - 4 \times 15 = 40 \)
\( \displaystyle |e_D| = \frac{4 \times 15}{40} = 1.5 \)
After the rise in income:
\( \displaystyle q = 120 - 4 \times 15 = 60 \)
\( \displaystyle |e_D| = \frac{4 \times 15}{60} = 1 \)
At the same price, more is now demanded, so the same price change is a smaller percentage of the larger quantity. The elasticity falls from 1.5 to 1.
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 Δ Δ = –b.” “From (2.17), it is clear that the elasticity of demand is different at different points on a linear demand curve. …” “2.4.6 Movements along the Demand Curve and Shifts in the Demand Curve … Thus, any change in the price leads to movements along the demand curve. On the other hand, changes in any of the other things lead to a shift in the demand curve. …” |