Assume total productivity is given as Q = 1600L + +50L2 - 1.5L3 Determine the marginal...
Assume total productivity is given as Q = 1600L + +50L2 - 1.5L3
Determine the marginal productivity of the 10th worker and the average productivity of the first 10 workers.
Also, show the work for determining the number of labor to maximize productivity. How many units of our goods will be produced?
Homework Answers
We have Q = 1600L + +50L2 - 1.5L3
This gives MPL = dQ/dL = 1600 + 100L - 4.5L^2 and APL = Q/L = 1600 + 50L - 1.5L^2
MPL (L = 10) = 1600 + 100*(10) - 4.5*(10^2) = 2150 units
APL (L = 10) = 1600 + 50*10 - 1.5*(10^2) = 1950 units
To maximize productivity, MPL should be 0
This gives 1600 + 100L - 4.5L^2 = 0.
This happens at L = 33 where MPL becomes 0
At L = 33, a total of 1600*33 + 50*33^2 - 1.5*(33^3) = 53344.50 units are produced.
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