In a perfectly competitive market with free entry and exit, all firms are identical. The long run total cost of each firm is shown below, and the market demand is q = 200 - 4p.
| Output per firm (units) | 1 | 2 | 3 | 4 | 5 |
|---|---|---|---|---|---|
| Long run TC of a firm (Rs) | 30 | 44 | 54 | 68 | 90 |
What are the equilibrium price and the number of firms?
Answer & explanation
Correct answer: option 4
The correct answer is Option (4) → Rs 17; 33 firms
With free entry and exit, price equals the minimum of LRAC. Demand at that price gives market quantity, and the number of firms is market quantity ÷ output of one firm.
Given:
Market demand: q = 200 − 4p
Long run TC for 1 to 5 units = Rs 30, 44, 54, 68, 90
\( \displaystyle LRAC = \frac{TC}{q}: \; 30,\; 22,\; 18,\; 17,\; 18 \)
Minimum LRAC is Rs 17, at 4 units per firm.
\( \displaystyle q = 200 - 4 \times 17 = 132 \)
\( \displaystyle n = \frac{132}{4} = 33 \)
The price is Rs 17 with 33 firms.
Option (1) Rs 14; 36 firms — Rs 14 is a marginal cost (68 − 54), not the minimum average cost.
Option (2) Rs 10; 40 firms — Rs 10 is also a marginal cost (54 − 44), not the minimum average cost.
This question uses Market Equilibrium (free entry) and Production and Costs (LRAC from total cost) together.
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. …” Production and Costs: “3.7.2 Long Run Costs In the long run, all inputs are variable. There are no fixed costs. The total cost and the total variable cost therefore, coincide in the long run. Long run average cost (LRAC) is defined as cost per unit of output, i.e.” |