Question

Suppose the short run production function can be represented by

Q=60,000L^2-1000L^3 then, determine

A) the level labor employement that maximazes the level of output

B) the level of employment that maximazes APL and the maximum APL

Answer 1

A) The level labor employement that maximazes the level of output is:

$MPL = Q'(L) = 120,000L - 3,000L^2 = 0,$

L(40 - L) = 0,

L = 0 (does not apply), L = 40 units.

B) The level of employment that maximazes APL is:

$APL = Q/L = 60,000L - 1,000L^2 = 0,$

L(60 - L) = 0,

L = 0 (does not apply), L = 60 units.

The maximum APL is:

$APL = 60,000×60 - 1,000×60^2 = 0.$