Question #68113

4. Determine the returns to scale for each of the following production functions:
a. Q = 50L + 6K + 8LK

Expert's answer

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.

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.

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