Skip to content

CA Foundation · Business Economics · Theory of Production and Cost

A production function is Q = 4L^0.5 K^0.5 for a firm in Ludhiana. If the firm increases both L and K by the same factor of 4, by what factor does output change, and which type of returns to scale is shown?

Output rises 4 times, showing constant returns to scale. The exponents on labour and capital sum to 1, so scaling both inputs by 4 scales output by 4^(0.5+0.5), which equals 4. Output changes in exactly the same proportion as inputs.

  1. AOutput rises 4 times; constant returns to scaleCorrect
  2. BOutput rises 2 times; decreasing returns to scale
  3. COutput rises 8 times; increasing returns to scale
  4. DOutput rises 16 times; increasing returns to scale

Explanation

Multiply L and K by 4: Q' = 4(4L)^0.5(4K)^0.5 = 4 x 4^0.5 x 4^0.5 x L^0.5 K^0.5 = 4 x 4 x (L^0.5 K^0.5) = 4 times the original Q. The exponents sum to 0.5+0.5 = 1, so returns are constant. Option B wrongly takes the square root of 4 only for one factor.

Did you get it right without looking?

One question tells you little. A timed set on Theory of Production and Cost shows your real accuracy, how long you take and where you lose marks.

Practise Theory of Production and CostFree diagnostic mock

More Theory of Production and Cost questions