2 marks, −0.667MicroeconomicsPerfect competitionMarket equilibrium and comparative staticsModerateabout 2 min

IIT JAM 2021 Question 17: Perfect competition

Two firms with identical technology have cost $C_i(q_i) = q_i^2$ . Market demand is $p = 100 - q$ with $q = q_1 + q_2$ . Assuming the firms are price takers, the competitive equilibrium $(p, q)$ is

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Answer and worked solution

Answer: (D)

As price takers each firm sets $p = MC_i = 2q_i$ , so $q_i = p/2$ and total supply is $q = q_1 + q_2 = p$ .

Substituting into demand $p = 100 - q = 100 - p$ gives $2p = 100$ , so $p = 50$ and $q = 50$ . The answer is (D).

The trap: (A)

p = 80,\ q = 20

Under price-taking the firms equate price to marginal cost, not exercise the market power that would push price toward 80; the competitive outcome is $p = q = 50$ .

Plain-text version

Two firms with identical technology have cost Cᵢ(qᵢ) = qᵢ². Market demand is p = 100 - q with q = q₁ + q₂. Assuming the firms are price takers, the competitive equilibrium (p, q) is (A) p = 80, q = 20 (B) p = 20, q = 80 (C) p = 200/3, q = 100/3 (D) p = 50, q = 50

Also written as: Two firms with identical technology have cost C_i(q_i) = q_i^2. Market demand is p = 100 - q with q = q_1 + q_2. Assuming the firms are price takers, the competitive equilibrium (p, q) is

Perfect competition has come up 115 times in 7 exams since 2006.

What this question tests

This question is on Market equilibrium and comparative statics, part of Perfect competition in Microeconomics.

Finding equilibrium from demand and supply and tracing how it moves when either curve shifts.

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