Question

You are given the production function: Q(K,L)=10KαLβ

Does the above function exhibit increasing, decreasing or constant return to scale? Illustrate why and explain what this means.

Answer 1

Production function is given as;

$Q(K,L)=10K^αL^β$

For the determination of the type of return to scale we have to make certain changes in inputs, let say both the inputs are changed by x.

Then,

$Q(xK,xL)=10(xK)^α(xL)^β$

$= 10 (x)^α + β (K^αL^β)$

$= (x)^α + β(10K^αL^β)$

$= (x)^α + β Q(K,L)$

Here return to scale depend upon the α + β

We could have three cases because the value of α, β are not specified

If (α + β) = 1 constant return to scale

If (α + β) > 1 positive return to scale

If (α + β) < 1 negative return to scale