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IAI Actuarial Core Principles · Business Economics · Production, costs, revenue and profit in price and output decisions

A monopolist faces the demand curve P = 100 - 2Q, where P is in rupees. What is its marginal revenue at Q = 10?

Marginal revenue at Q = 10 is Rs 60. Total revenue is 100Q - 2Q^2, so marginal revenue is its derivative, 100 - 4Q, which gives 100 - 40 = Rs 60. Marginal revenue falls twice as fast as price.

  1. ARs 20
  2. BRs 60
  3. CRs 80
  4. DRs 40Correct
  5. Rs 100

Explanation

TR = PQ = 100Q - 2Q^2. MR = dTR/dQ = 100 - 4Q. At Q = 10, MR = 100 - 40 = Rs 60... checking: 100 - 40 = 60, so the key must be Rs 60.

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