A market has 10 identical firms, each with supply q = 2p - 20 for p ≥ 10. The market demand is q = 400 - 10p. If 5 of the firms leave the market, what are the new equilibrium price and the output of each remaining firm?
Answer & explanation
Correct answer: option 4
The correct answer is Option (4) → Rs 25; 30 units
Market supply is the sum of the firms’ supplies. With fewer firms, market supply shifts left, so the price rises.
Given:
Each firm: q = 2p − 20
Market demand: q = 400 − 10p
Firms: 10, then 5
With 10 firms, market supply = 20p − 200:
\( 20p - 200 = 400 - 10p \)
\( 30p = 600 \)
\( p = 20 \)
With 5 firms, market supply = 10p − 100:
\( 10p - 100 = 400 - 10p \)
\( 20p = 500 \)
\( p = 25 \)
\( \displaystyle \text{Each remaining firm} = 2 \times 25 - 20 = 30 \)
The price rises to Rs 25 and each remaining firm produces 30 units (market quantity falls from 200 to 150). Each firm sells more than before, because it moves up its own supply curve.
NCERT (2026-27): “Supply Shift … Let us discuss the impact of an increase in the number of firms. Since at each price now more firms will supply the commodity, the supply curve shifts to the right but it does not have any effect on the demand curve. This example can be illustrated by Figure 5.3(b) where the supply curve shifts from SS0 to SS1 whereas the demand curve remains unchanged at DD0. From the figure, we can say that there will be a decrease in price of the commodity and increase in the quantity produced compared to the initial situation.” |