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This is a short-run production function where Q = units produced per month:
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Q = 150 K L + 6 K L^2 – 0.1 K L^3 ( Assume K is constant at 3 units)
- 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) - At what level of labor utilization is the average productivity of labor maximized?
- After what level of labor utilization (and total units produced per month) does the Law of diminishing Marginal Returns Take effect?
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https://brainmass.com/business/business-management/production-functions-in-the-short-term-117881
Solution Preview - Q = 150 K L + 6 K L^2 – 0.1 K L^3
Given K=3
we have
Q=1503L+63L^2 – 0.13L^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 + 182L -0.33L^2=0
450+36L-0.9L^2=0
Solve …
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