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Worked Examples · Example 2
Q.

A firm's labour and capital, and the resulting output, are given below. Both inputs are increased in the same proportion each time. Identify the law of returns to scale operating (a) between the first and second rows, and (b) between the second and third rows.

LabourCapitalOutput
2210
4422
8840
Tamil Nadu DgeTextbookSubjectiveImportance★★★★★
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✓ Free question

Both labour and capital are doubled at each step, so the test is simply whether output MORE than doubles, EXACTLY doubles, or LESS than doubles.

  1. From (2,2) to (4,4): inputs increase by a factor of 42=2\dfrac{4}{2}=2. Output increases by a factor of 2210=2.2\dfrac{22}{10}=2.2. Since 2.2>22.2>2, output has grown in a GREATER proportion than the inputs — this is Increasing Returns to Scale.
  2. From (4,4) to (8,8): inputs again increase by a factor of 84=2\dfrac{8}{4}=2. Output increases by a factor of 4022=1.82\dfrac{40}{22}=1.82. Since 1.82<21.82<2, output has grown in a SMALLER proportion than the inputs — this is Diminishing Returns to Scale. This is a realistic pattern: the firm enjoys Increasing Returns to Scale while it is still small enough to benefit from greater specialisation and better use of indivisible factors, but as it grows very large, coordination difficulties set in and Diminishing Returns to Scale take over.
    ✓Final answer

    (a) Increasing Returns to Scale (output ratio 2.2>2.2> input ratio 22). (b) Diminishing Returns to Scale (output ratio 1.82<1.82< input ratio 22).

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