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CA Foundation · Business Economics · Theory of Production and Cost

A firm has the production function Q = 2L^0.5 K^0.5. With L = 16 and K = 25, output is 40 units. If the firm triples both L and K to 48 and 75, output will be:

Output will be 120 units. The exponents 0.5 and 0.5 sum to one, so the function has constant returns to scale and tripling both inputs triples output from 40 to 120.

  1. A120 units, since returns to scale are constantCorrect
  2. B40 × √3 ≈ 69.3 units, since returns are decreasing
  3. C360 units, since returns are increasing
  4. D80 units, since output only doubles

Explanation

Check the base: 2 × √16 × √25 = 2 × 4 × 5 = 40. Tripling both inputs gives 2 × (3L)^0.5 (3K)^0.5 = 2 × 3 × L^0.5 K^0.5 = 3 × 40 = 120. The exponents sum to 1, so returns to scale are constant. The 69.3 figure wrongly scales output by √3, treating only one input as tripled.

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