2 marksMicroeconomicsMonopoly and price discriminationMulti-plant and multi-product monopolyHardabout 3 min

IIT JAM 2021 Question 53: Monopoly and price discrimination

A firm has two plants with $TC_1 = 500 + 30Q_1$ and $TC_2 = 1500 + 20Q_2$ . Demand is $Q^d = 150 - \dfrac{P}{3}$ . The value of $Q_1$ that maximizes the firm's profit is _______ (in integer).

Answer and worked solution

Answer: 0

The two plants have constant marginal costs $30$ (plant 1) and $20$ (plant 2). A profit-maximising firm produces in the cheaper plant, and with no capacity constraint it uses only plant 2.

Marginal revenue is set equal to the lower marginal cost of $20$ , and plant 1 (marginal cost $30$ ) is never used. So $Q_1 = 0$ . The answer is $0$ .

Plain-text version

A firm has two plants with TC₁ = 500 + 30Q₁ and TC₂ = 1500 + 20Q₂. Demand is Q^d = 150 - P/3. The value of Q₁ that maximizes the firm's profit is _ (in integer).

Also written as: A firm has two plants with TC_1 = 500 + 30Q_1 and TC_2 = 1500 + 20Q_2. Demand is Q^d = 150 - P/3. The value of Q_1 that maximizes the firm's profit is _ (in integer).

Monopoly and price discrimination has come up 128 times in 7 exams since 2004.

What this question tests

This question is on Multi-plant and multi-product monopoly, part of Monopoly and price discrimination in Microeconomics.

How a monopolist allocates output across plants, markets or products.

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