In the following production functions output q is a function

In the following production functions, output q is a function of capital K and labour L. Do the following functions exhibit increasing, constant, or decreasing returns to scale?

Explain your answers.

a) q = 2L + 6K

b) q = ( 2L + 2K )^1/2

c) q = 3LK²

Solution

a) q = 2L + 6K

This function exhibits constant returns to scale. Because when the inputs are doubled, output will double.

Let, L = 2 & K = 2

q = 2(2) + 6(2) = 16

Now, let the inputs are doubled.

Then, q = 2(4) + 6(4) = 32

b) q = ( 2L + 2K )^1/2

This function exhibits decreasing returns to scale. Because when the inputs are doubled, output will less than double.

Let, L = 2 & K = 2

q = ( 2*2+ 2*2 )^1/2 = 2.83

Now, let the inputs are doubled.

q = ( 2*4+ 2*4 )^1/2 = 4 (it means output is less than double)

c) q = 3LK²

This function exhibits increasing returns to scale. Because when the inputs are doubled, output will more than double.

Let, L = 2 & K = 2

q = 3LK² = 3(2)(2)² = 24

Now, let the inputs are doubled.

q = 3LK² = 3(4)(4)² = 192   (it means output is more than double)