Determine which of the following production functions exhibit decreasing returns to scale,
increasing returns to scale, or constant returns to scale.
Q = K/(L)^2
Q = 4K + 2L
Q = a KL
Q = K/(L)2
Let's double the inputs, Q' = 2K/(2L)2
Q' = 1/2(K/L2)
Q'=1/2Q
Doubling the input , leads to decrease in output to half, so this is decreasing returns to scale where the increase in input leads to decrease in output.
Q = 4K + 2L
Q' = 2(4K + 2L)
Q' = 8K + 4L
Q' = 2(4K + 2L)
Q' = 2Q
Doubling the input , leads to double in output, so this is constant returns to scale where the increase in input leads to same increase in output.
Q = a KL
Q ' = a2K 2L
Q' = 4aKL
Q' = 4Q
Doubling the input , leads to increase in output four times, so this is increasing returns to scale where the increase in input leads to large increase in output.
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