In a perfectly competitive market with free entry and exit, every firm has a minimum average cost of Rs 20, at which it produces 10 units. The market demand is q = 300 - 5p. Then two changes happen together: a rise in input prices raises the minimum average cost to Rs 24 (each firm still produces 10 units there), and a rise in income changes the demand to q = 340 - 5p. What are the new market price and number of firms?
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → Rs 24; 22 firms
With free entry and exit, the price settles at the minimum average cost of the firms. Demand at that price fixes the market quantity, and number of firms = market quantity ÷ output of one firm.
Given:
New minimum AC = Rs 24, at 10 units per firm
New demand: q = 340 − 5p
\( \displaystyle p = 24 \)
\( \displaystyle q = 340 - 5 \times 24 \)
\( \displaystyle q = 340 - 120 = 220 \)
\( \displaystyle n = \frac{220}{10} = 22 \)
The price is Rs 24 and there are 22 firms. Both changes act together here.
Option (2) Rs 20; 24 firms — this takes only the demand rise.
Option (4) Rs 24; 18 firms — this takes only the cost rise.
NCERT (2026-27): “5.1.2 Market Equilibrium: Free Entry and Exit From the above, it follows that the equilibrium price will be equal to the minimum average cost of the firms. In equilibrium, the quantity supplied will be determined by the market demand at that price so that they are equal. …” “… Therefore, the equilibrium number of firms in the market is equal to the number of firms required to supply q0 output at p0, each in turn supplying q0f amount at that price. …” |