2 marks, −0.667MicroeconomicsMonopoly and price discriminationMonopoly equilibrium and marginal revenueHardabout 2 min

IIT JAM 2021 Question 11: Monopoly and price discrimination

A monopoly canteen serves two groups with demands $Q_X = 200 - 4P$ and $Q_Y = 300 - P$ , where $P$ is the uniform price. The unit cost of each meal is Rs. 50. The value of $P$ (in Rs.) that maximizes the canteen's profit is

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Answer and worked solution

Answer: (D)

Group $X$ only buys while $P \le 50$ (since $Q_X = 200 - 4P \ge 0$ ). On the joint segment the unconstrained optimum ( $P = 75$ ) is infeasible, and profit there is at most zero at $P = 50$ .

For $P > 50$ only group $Y$ remains, with $Q_Y = 300 - P$ . Maximising $(P - 50)(300 - P)$ gives $P = 175$ , with profit $125 \times 125 = 15625 > 0$ . So the profit-maximising price is Rs. 175, option (D).

The trap: (A) 75

The naive first-order condition on the combined demand gives 75, but at that price group X has already dropped out; accounting for the kink moves the optimum to 175.

Plain-text version

A monopoly canteen serves two groups with demands Q_X = 200 - 4P and Q_Y = 300 - P, where P is the uniform price. The unit cost of each meal is Rs. 50. The value of P (in Rs.) that maximizes the canteen's profit is (A) 75 (B) 50 (C) 125 (D) 175

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What this question tests

This question is on Monopoly equilibrium and marginal revenue, part of Monopoly and price discrimination in Microeconomics.

How a monopolist sets price and output where marginal revenue equals marginal cost.

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