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CMA Foundation · Fundamentals of Business Economics and Management · Theory of Production

A firm's production function is Q = 6L^0.5 K^0.5, where L is labour and K is capital. If both L and K are quadrupled, by what factor does output change?

Output becomes four times. The exponents of labour and capital add up to one, which means constant returns to scale. Quadrupling both inputs multiplies output by 4 raised to the power of 1, giving four times the original output.

  1. AIt becomes 2 times
  2. BIt becomes 4 timesCorrect
  3. CIt becomes 8 times
  4. DIt becomes 16 times

Explanation

The exponents sum to 0.5 + 0.5 = 1, so the function shows constant returns to scale. Check: new Q = 6(4L)^0.5(4K)^0.5 = 6 x 2 x 2 x L^0.5 K^0.5 = 4Q. The factor of 16 wrongly applies 4 x 4 without taking the powers.

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