1 markMicroeconomicsPerfect competitionMarket equilibrium and comparative staticsModerateabout 2 min

IIT JAM 2022 Question 48: Perfect competition

The cost function for firm $i$ is $C_i = 0.25q_i^2 + 2q_i + 5$ , $i = 1, \ldots, 150$ . The aggregate inverse demand is $P = 10 - 0.01Q$ , where $Q$ is aggregate output. Assuming perfect competition, the equilibrium quantity is _______ (in integer).

Answer and worked solution

Answer: 4 to 4 or 600 to 600

Each firm sets $P = MC_i = 0.5q_i + 2$ , so its supply is $q_i = 2P - 4$ , and aggregate supply is $Q = 150(2P - 4) = 300P - 600$ .

Combining with inverse demand $P = 10 - 0.01Q$ gives $Q + 600 = 3000 - 3Q$ , so $Q = 600$ . At that quantity the price is $P = 4$ and each firm produces $q_i = 4$ . The exam accepts either the aggregate output $600$ or the per-firm output $4$ (both equal the price too).

Plain-text version

The cost function for firm i is Cᵢ = 0.25qᵢ² + 2qᵢ + 5, i = 1, …, 150. The aggregate inverse demand is P = 10 - 0.01Q, where Q is aggregate output. Assuming perfect competition, the equilibrium quantity is _ (in integer).

Also written as: The cost function for firm i is C_i = 0.25q_i^2 + 2q_i + 5, i = 1,..., 150. The aggregate inverse demand is P = 10 - 0.01Q, where Q is aggregate output. Assuming perfect competition, the equilibrium quantity is _ (in integer).

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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Question from the IIT JAM 2022 paper. Solutions are TestStop's own. Not affiliated with or endorsed by any examination authority.