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

A monopolist insurer-like seller faces the demand curve P = 200 - 2Q and has constant marginal cost of Rs 40 per unit. What price will it charge at the profit-maximising output?

The monopolist charges Rs 120. Marginal revenue is 200 - 4Q; equating it to marginal cost of 40 gives output of 40 units, and the demand curve then gives a price of 200 - 80 = Rs 120.

  1. ARs 40
  2. BRs 80
  3. CRs 100
  4. DRs 120Correct
  5. Rs 160

Explanation

Total revenue = 200Q - 2Q², so MR = 200 - 4Q. Setting MR = MC gives 200 - 4Q = 40, so Q = 40. Price = 200 - 2(40) = Rs 120. Rs 80 comes from using the demand slope instead of the MR slope (Q = 80 gives P = 40, the competitive result is Rs 40).

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