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

A firm has the production function Q = L^0.6 K^0.7. If it increases both L and K by the same proportion, which statement is correct, and what is the combined effect of doubling both inputs on the output multiple (approximately, given 2^1.3 is about 2.46)?

The firm enjoys increasing returns to scale, and doubling both inputs raises output to about 2.46 times. The exponents sum to 1.3, which exceeds one, so output grows more than proportionately. The multiple is 2 raised to 1.3, not 1.3 itself.

  1. ADecreasing returns to scale; output rises to about 1.74 times
  2. BConstant returns to scale; output exactly doubles
  3. CIncreasing returns to scale; output rises to about 2.46 timesCorrect
  4. DIncreasing returns to scale; output rises to about 1.3 times

Explanation

The sum of exponents is 0.6 + 0.7 = 1.3, which is more than 1, so the function shows increasing returns to scale. Doubling both inputs multiplies output by 2^0.6 x 2^0.7 = 2^1.3, about 2.46. Option D wrongly uses the exponent sum itself as the output multiple.

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