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

A Chennai insurer's back-office production function is Q = L^0.6 K^0.5. If it raises both L and K by 10%, which description of returns to scale and the approximate effect on output is best?

Increasing returns to scale, with output up by about 11%. The exponents 0.6 and 0.5 sum to 1.1, which is above one, so a 10% rise in all inputs raises output by 1.1 to the power 1.1, roughly 1.11 times the original level.

  1. AConstant returns; output rises by about 10%
  2. BDecreasing returns; output rises by about 5.5%
  3. CIncreasing returns; output rises by about 11%Correct
  4. DIncreasing returns; output rises by about 21%
  5. Decreasing returns; output rises by about 11%

Explanation

The exponents sum to 1.1, which exceeds 1, so returns to scale are increasing. Output scales by 1.1^1.1, approximately 1.11, an increase of about 11%. Option four wrongly squares the factor; decreasing returns would need exponents summing to less than 1.

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