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Returns to Scale

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Determine whether the following production functions exhibit constant, increasing, or decreasing returns to scale.
A. Q = 10X + 4Y + 0.25Z
B. Q = 12L + 5K + 500
C. Q = 4A + 14B + 3AB
D. Q = 5L2 + 5LK + 5K2
E. Q = 3L0.3K0.4

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The expert examines the returns to scales.

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Determine whether the following production functions exhibit constant, increasing, or decreasing returns to scale.

A. Q = 10X + 4Y + 0.25Z

Let X = Y = Z = 100, so output is:
Q1 = 10(100) + 4(100) + 0.25(100) = 1,425
If we increase all inputs by 10% output becomes:
Q2 = 10(110) + 4(110) + 0.25(110) = 1,567.50

A 10% increase in inputs results in a 10% increase in output
(Q2/Q1 = 1,567.50/1,425 = 1.10). The output elasticity is 1 and therefore this production system exhibits constant returns to ...

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