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Questions › GATE › GATE 2021 › Q6
2 marks, −0.667Microeconomics › Monopoly and price discrimination › Monopoly equilibrium and marginal revenueModerateabout 2 min

GATE 2021 Question 6: Monopoly and price discrimination

XYZ Co. Ltd. is a costless monopoly from suburban Mumbai producing and selling exotic mushrooms. The demand for mushrooms is given by

Q=700−100PQ=700-100PQ=700−100P

Do you agree that XYZ will have a maximum possible total revenue of ₹1500?

Tap an option to check your answer.

Answer and worked solution

Answer: (B)

Inverse demand: P=7−Q100P = 7-\dfrac{Q}{100}P=7−100Q​ (from Q=700−100PQ=700-100PQ=700−100P).

TR=PQ=(7−Q100)Q=7Q−Q2100TR = PQ = \left(7-\frac{Q}{100}\right)Q = 7Q-\frac{Q^2}{100}TR=PQ=(7−100Q​)Q=7Q−100Q2​

Maximizing: d(TR)dQ=7−2Q100=0⇒Q=350\dfrac{d(TR)}{dQ} = 7-\dfrac{2Q}{100}=0 \Rightarrow Q=350dQd(TR)​=7−1002Q​=0⇒Q=350.

P=7−350100=7−3.5=3.5P = 7-\frac{350}{100} = 7-3.5 = 3.5P=7−100350​=7−3.5=3.5

TRmax=3.5×350=1225TR_{max} = 3.5\times350 = 1225TRmax​=3.5×350=1225

Since the maximum possible total revenue (₹1225) is less than the stated ₹1500, the correct answer is (B): No, the maximum possible total revenue is less than ₹1500.

The trap: (A) Yes, the maximum possible total revenue is ₹1500

Students who don't actually work out the revenue-maximizing quantity and price (e.g., just estimating roughly or checking a specific arbitrary price point instead of finding the true maximum via calculus) might accept the ₹1500 figure at face value without verifying it numerically.

Plain-text version

XYZ Co. Ltd. is a costless monopoly from suburban Mumbai producing and selling exotic mushrooms. The demand for mushrooms is given by Q=700-100P Do you agree that XYZ will have a maximum possible total revenue of ₹1500? (A) Yes, the maximum possible total revenue is ₹1500 (B) No, the maximum possible total revenue is less than ₹1500 (C) No, the maximum possible total revenue is more than ₹1500 (D) No, the maximum possible total revenue cannot be estimated

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

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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