Question

Assume a​ Cobb-Douglas production function of the​ form: q equals 10 Upper L Superscript 0.33 Baseline Upper K Superscript 0.75. What type of returns to scaleLOADING... does this production function​ exhibit?

Answer 1

Answer:

Since 0.33 + 0.75 = 1.08 is greater than one, this production function therefore exhibits increasing returns to scale.

Explanation:

From the question, we have the following restated equation:

$q=10L^{0.33} K^{0.75}$

Where q is the output, and L and K are inputs

To determine the types of returns to scale, we increase each of L and K inputs by constant amount c as follows:

$q = 10(cL)^{0.33}(cK)^{0.75}$

We can now solve as follows;

$q = 10c^{0.33+0.75} L^{0.33}K^{0.75}$

$q=c^{1.08} L^{0.33} K^{0.75}$

Since 0.33 + 0.75 = 1.08 is greater than one, this production function therefore exhibits increasing returns to scale.