2 marksMicroeconomicsPerfect competitionProfit maximisation and the competitive firmHardabout 3 min

IIT JAM 2022 Question 60: Perfect competition

Two firms $F_1$ and $F_2$ produce homogeneous products with inverse demand $p = 120 - 0.5(q_1 + q_2)$ . Costs are $C_1 = 20q_1$ and $C_2 = 10 + 0.5q_2^2$ . Assuming a competitive situation, the total profit earned by both firms is _______ (in integer).

Answer and worked solution

Answer: 190 to 190 or 4790 to 4790

Under a competitive (price equals marginal cost) situation, $F_1$ has constant $MC_1 = 20$ , so the market price is $p = 20$ . $F_2$ has $MC_2 = q_2$ , so $q_2 = p = 20$ .

Inverse demand $20 = 120 - 0.5(q_1 + q_2)$ gives $q_1 + q_2 = 200$ , so $q_1 = 180$ . Profits are $\pi_1 = 20(180) - 20(180) = 0$ and $\pi_2 = 20(20) - (10 + 0.5\cdot400) = 400 - 210 = 190$ . Total profit is $190$ ; the exam also accepts an alternative reading valued at $4790$ .

Plain-text version

Two firms F₁ and F₂ produce homogeneous products with inverse demand p = 120 - 0.5(q₁ + q₂). Costs are C₁ = 20q₁ and C₂ = 10 + 0.5q₂². Assuming a competitive situation, the total profit earned by both firms is _ (in integer).

Also written as: Two firms F_1 and F_2 produce homogeneous products with inverse demand p = 120 - 0.5(q_1 + q_2). Costs are C_1 = 20q_1 and C_2 = 10 + 0.5q_2^2. Assuming a competitive situation, the total profit earned by both firms is _ (in integer).

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

What this question tests

This question is on Profit maximisation and the competitive firm, part of Perfect competition in Microeconomics.

How a price-taking firm picks output where price equals marginal cost, and when it breaks even or shuts down.

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