Question

4. Determine the returns to scale for each of the following production functions:

a. Q = 50L + 6K + 8LK

Answer 1

Suppose our inputs are capital or labor, and we double each of these (m = 2), we want to know if our output will more than double, less than double, or exactly double.
Q = 50L + 6K + 8LK,
Q' = 50L*m + 6K*m + 8LK*m^2,
Q' = m*(50L + 6K + 8LK*m), so Q' > Q more than in m = 2 times.
Our new production has increased by more than m, so we have increasing returns to scale.