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

A Bengaluru fintech has total cost TC = 20,000 + 100Q + 0.5Q² (rupees) in the short run. At what output is average total cost minimised, and what is the minimum average total cost?

Average total cost is minimised where it equals marginal cost, giving Q squared equal to 40,000, so output is 200 units. At that output average total cost is Rs 100 plus Rs 100 plus Rs 100, which is Rs 300, matching marginal cost of Rs 300.

  1. AQ = 150; ATC = Rs 300
  2. BQ = 200; ATC = Rs 300Correct
  3. CQ = 200; ATC = Rs 400
  4. DQ = 100; ATC = Rs 350
  5. Q = 400; ATC = Rs 300

Explanation

ATC = 20,000/Q + 100 + 0.5Q. MC = 100 + Q. Setting MC = ATC gives Q = 20,000/Q + 0.5Q, so 0.5Q = 20,000/Q, Q² = 40,000, Q = 200. ATC = 100 + 100 + 100 = Rs 300. Check: MC at 200 is Rs 300, equal to ATC. Q = 150 gives ATC 133.3+100+75 = 308.3, higher.

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