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

A Coimbatore pump manufacturer uses the production function Q = 4L^0.5 K^0.5, where L is labour and K is capital. If it triples both L and K, what happens to output?

Output becomes exactly three times the original. The exponents add up to one, so the function is homogeneous of degree one and shows constant returns to scale. Tripling both labour and capital therefore triples output, not nine times or any other multiple.

  1. AOutput rises to 9 times the original
  2. BOutput rises to 3 times the originalCorrect
  3. COutput rises to 6 times the original
  4. DOutput rises to 1.5 times the original

Explanation

Exponents sum to 0.5 + 0.5 = 1, so the function is homogeneous of degree 1 and shows constant returns to scale. Tripling inputs gives Q' = 4(3L)^0.5(3K)^0.5 = 3 x 4L^0.5K^0.5, i.e. 3 times. Option A wrongly squares the factor by treating the exponents as adding to 2.

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