In the following production functions output q is capital K

In the following production functions, output q is capital K and labour L. Do the following functions exhibit increasing, constant, or decreasing returns to scale? Explain your answer:

Solution

A function exhibits constant returns to scale if multiplying the inputs by a certain factor increases the output by the same factor. A function exhibits increasing returns to scale if multiplying the inputs by a certain factor increases the output by more than the same factor. A function exhibits decreasing returns to scale if multiplying the inputs by a certain factor increases the output by less than the same factor.

Based on this definition,

a. Constant returns to scale

b. Decreasing returns to scale

c. Increasing returns to scale

d. Decreasing returns to scale

e. Decreasing returns to scale

f. Constant returns to scale

Explanation calculation of (a) is below for reference:

q = 2L+6K

Multiply L and K by 2:

q\' = 2(2L)+6(2K)

q\' = 4L+12K

q\' = 2(2L+6K)

q\' = 2q

Thus, constant returns to scale exist.

Follow the same steps in rest of hte parts as well.