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# Production Functions in the Short Term

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This is a short-run production function where Q = units produced per month:

Q = 150 K L + 6 K L^2 - 0.1 K L^3 ( Assume K is constant at 3 units)

1. At what level of labor utilization is total production maximized? What is the maximum level of total production that this firm can attain per month?
(Rounded to the nearest full unit)

2. At what level of labor utilization is the average productivity of labor maximized?

3. After what level of labor utilization (and total units produced per month) does the Law of diminishing Marginal Returns Take effect?

#### Solution Preview

1. Q = 150 K L + 6 K L^2 - 0.1 K L^3
Given K=3
we have
Q=150*3*L+6*3*L^2 - 0.1*3*L^3=450L+18L^2-0.3L^3
For production maximization differentiate the equation with respect to L and equate to zero, we get
dQ/dL = 450 + 18*2*L -0.3*3*L^2=0
450+36L-0.9L^2=0
Solve ...

#### Solution Summary

The solution shows production functions in the short term.

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