Question

Determine which of the following production functions exhibit decreasing returns to scale, increasing returns to scale,...

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

Homework Answers

Answer #1

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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