A market has 100 identical consumers, each with demand q = 10 - p, and 50 identical firms, each with supply q = p - 1 for p ≥ 1. What is the equilibrium price, and how much does each firm sell?
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → Rs 7; 6 units
Add up the consumers to get market demand and the firms to get market supply; equilibrium is where they are equal.
Given:
100 consumers, each q = 10 − p
50 firms, each q = p − 1
\( \displaystyle \text{Market demand} = 100(10 - p) = 1000 - 100p \)
\( \displaystyle \text{Market supply} = 50(p - 1) = 50p - 50 \)
\( 1000 - 100p = 50p - 50 \)
\( 150p = 1050 \)
\( p = 7 \)
\( \displaystyle \text{Each firm} = 7 - 1 = 6 \)
The price is Rs 7 and each firm sells 6 units (market quantity 300; each consumer buys 3).
NCERT (2026-27): “5.1.1 Market Equilibrium: Fixed Number of Firms Recall that in Chapter 2 we have derived the market demand curve for price-taking consumers, and for price-taking firms the market supply curve was derived in Chapter 4 under the assumption of a fixed number of firms. In this section with the help of these two curves we will look at how supply and demand forces work together to determine where the market will be in equilibrium when the number of firms is fixed. …” “… Graphically, an equilibrium is a point where the market supply curve intersects the market demand curve because this is where the market demand equals market supply. …” |