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

A Chennai claims-processing centre has the long-run production function Q = 2L^0.4K^0.4, where L is labour and K is capital. If the centre doubles both L and K, what happens to output?

Output rises by 2^0.8, about 1.74 times, which is less than double. The exponents on labour and capital sum to 0.8, below 1, so the function shows decreasing returns to scale regardless of the multiplicative constant.

  1. AOutput doubles exactly
  2. BOutput rises by a factor of 2^0.8, which is less than doubleCorrect
  3. COutput rises by a factor of 2^1.2, which is more than double
  4. DOutput rises by a factor of 4
  5. Output stays the same

Explanation

Scaling both inputs by 2 multiplies output by 2^0.4 x 2^0.4 = 2^0.8, about 1.74. The exponents sum to 0.8, which is less than 1, so there are decreasing returns to scale. The constant 2 does not affect the scale factor, so doubling exactly is wrong.

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