Question

2. A firm produces according to the following production function: Q = K0.4L0.5. MCK is $10 per K, and MCL is $8 per L. What sort of returns to scale does the firm face? Motivate your answer

Answer 1

The sort of returns to scale the firm face is a decreasing return to scale.

Step-by-step explanation:

The production function is correctly restated as follows:

`Q = K^(0.4)L^(0.5)` .................................. (1)

To determine the type of return to scale, the input usages K and L are scaled by the multiplicative factor ∝, and substituting it into equation (1), we can have the following:

`Q =( \alpha K)^(0.4)(\alpha L)^(0.5)`

`Q = \alpha^(0.4) K^(0.4)\alpha^(0.5) L^(0.5)`

`Q = \alpha^(0.4) \alpha^(0.5)K^(0.4) L^(0.5)`

`Q = \alpha^(0.4)^(+0.5)K^(0.4) L^(0.5)`

`Q = \alpha^(0.9)K^(0.4) L^(0.5)`

Since the sum of the exponents of the multiplicative factor ∝ is 0.9 which is less than 1, the sort of returns to scale the firm face is a decreasing return to scale.