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CA Foundation · Business Economics · Theory of Production and Cost

A firm's production function is Q = 2K·L with K fixed at 5 units in the short run, so Q = 10L. In the long run the firm doubles both K and L from K = 5, L = 4. What is the nature of returns to scale?

The firm has increasing returns to scale. Output is 40 at K=5 and L=4, and after doubling both inputs it becomes 160. Output quadruples when inputs merely double, so output rises more than proportionately.

  1. AIncreasing returns to scale, as output rises from 40 to 160Correct
  2. BConstant returns to scale, as output rises from 40 to 80
  3. CDecreasing returns to scale, as output rises from 40 to 120
  4. DIncreasing returns to scale, as output rises from 40 to 120

Explanation

Initial Q = 2×5×4 = 40. After doubling, K = 10 and L = 8, so Q = 2×10×8 = 160. Output rises fourfold while inputs only double, so returns to scale are increasing. Option 2 mistakenly treats the output as proportional to a single input.

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