Answer to Question #100971 in Microeconomics for Ayisanew

Question

A short run production function with single variable factor-Labor(L), given as follows: Q=60L²-2K³, then answer the following questions
A. Determined the level of lobor and capital which gives the maximum possible output
B. Compute Labor employment that corresponding with the maximum possible MPL and APL

Answer 1

A. The output is maximized when Q'(L) = MPL = 0, so:

Q'(L) = MPL = 120L - 2K^3 = 0,

L = K^3/60.

B. MPL and APL are maximized when MPL' = 0 and APL' = 0, so:

MPL'(L) = 120 - 2K^3 = 0,

K^3 = 60,

K = 3.91 units.

APL'(L) = 60 - 2K^3/L^2 = 0,

K^3/L^2 = 30,

L^2 = K^3/30.