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

Answer:

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

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.