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IAI Actuarial Core Principles · Business Economics · Profit maximisation under perfect competition and monopoly

A monopolist has demand P = 200 - Q, where P is in rupees, and total cost C = 1,000 + 40Q. A regulator imposes a lump-sum annual licence fee of Rs 2,000 on the firm. What is the effect on the profit-maximising price and output?

Price and output are unchanged, and profit falls by exactly Rs 2,000. A lump-sum licence fee is a fixed cost that does not alter marginal cost or marginal revenue, so the MR = MC output of 80 units at Rs 120 stays optimal, and profit remains positive at Rs 3,400.

  1. APrice rises and output falls because costs have increased
  2. BPrice and output are unchanged, and profit falls by Rs 2,000Correct
  3. CPrice falls and output rises to absorb the fee
  4. DThe firm shuts down because profit becomes negative
  5. Output is unchanged but price rises by Rs 2,000

Explanation

MR = 200 - 2Q equals MC = 40 at Q = 80, giving P = Rs 120. A lump-sum fee is a fixed cost and leaves MC and MR unchanged, so output and price do not change. Profit before fee = 120x80 - (1,000+3,200) = 9,600 - 4,200 = Rs 5,400; after fee Rs 3,400, still positive so no shutdown.

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