Question

Given the following short run production function Q=12L²-4L³
what is the rang of feasible units of labor that determines second stage of production?

Answer 1

Q=12L²-4L³
In the beginning of the second stage of production marginal product equals average product: MP = AP,
MP = Q' = 24L - 12L^2,
AP = Q/L = 12L - 4L^2
12L - 4L^2 = 24L - 12L^2
8L^2 - 12L = 0
L1 = 0 (is not a route in our case), L2 = 1.5
In the end of the second stage MP = 0, so 24L - 12L^2 = 0
L1 = 0 (is not a route in our case), L2 = 2.
So the range is between 1.5 and 2 units of labor.