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

An insurer's demand for a product is P = 300 - 3Q. At which output is total revenue maximised, and what is the maximum total revenue (rupees)?

Total revenue is maximised at Q = 50 with TR of Rs 7,500. Setting marginal revenue, 300 - 6Q, to zero gives Q = 50, where price is Rs 150, so revenue is 150 x 50 = Rs 7,500, the point of unit elasticity.

  1. AQ = 50, TR = 7,500Correct
  2. BQ = 100, TR = 0
  3. CQ = 25, TR = 5,625
  4. DQ = 50, TR = 15,000
  5. Q = 75, TR = 5,625

Explanation

TR = 300Q - 3Q^2. MR = 300 - 6Q = 0 gives Q = 50. Then P = 150 and TR = 150 x 50 = 7,500. Check: at Q = 50 demand is unit elastic. Rs 15,000 wrongly uses P = 300.

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