A market has two groups of firms. Each of the 10 firms in group 1 supplies q = 2p - 10 for p ≥ 5, and each of the 5 firms in group 2 supplies q = 4p - 40 for p ≥ 10; below these prices they supply nothing. What is the price elasticity of the market supply at a price of Rs 15?
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → 2
Market supply is the horizontal sum of the firms’ supply curves. At Rs 15 both groups produce (15 is above 5 and above 10).
Given:
Group 1: 10 firms, each q = 2p − 10
Group 2: 5 firms, each q = 4p − 40
Price = Rs 15
\( Q = 10(2p - 10) + 5(4p - 40) \)
\( Q = 40p - 300 \)
At p = 15:
\( Q = 600 - 300 = 300 \)
\( \displaystyle e_S = \frac{\Delta Q}{\Delta p} \times \frac{p}{Q} \)
\( \displaystyle e_S = 40 \times \frac{15}{300} = 2 \)
The elasticity of market supply is 2; it needs both groups together.
Option (3) 1.5 — this is group 1 alone.
Option (4) 3 — this is group 2 alone.
NCERT (2026-27): “4.6 Market Supply Curve … Given p3, firm 1 supplies q3 units of output while firm 2 supplies q4 units of output. So, the market supply at price p3 is q5, where q5 = q3 + q4. …” “4.7 Price Elasticity of Supply The price elasticity of supply of a good measures the responsiveness of quantity supplied to changes in the price of the good. …” |