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

A Surat textile unit has the production function Q = 4L^0.5 K^0.5. If it doubles both labour L and capital K, what happens to output?

Output doubles. The exponents 0.5 and 0.5 sum to one, so scaling both inputs by two scales output by two to the power one, which is two. This is constant returns to scale. The factor 4 is just a constant and does not affect scaling.

  1. AOutput rises by a factor of about 1.41
  2. BOutput doubles, showing constant returns to scaleCorrect
  3. COutput rises by a factor of 4, showing increasing returns
  4. DOutput rises by 50%, showing decreasing returns
  5. Output stays unchanged because of the fixed multiplier 4

Explanation

Replace L and K with 2L and 2K: Q' = 4(2L)^0.5(2K)^0.5 = 4 x 2^(0.5+0.5) L^0.5 K^0.5 = 2Q. The exponents sum to 1, so returns to scale are constant. A factor of 1.41 would result from doubling only one input.

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