# Answer to Question #45437 in Economics of Enterprise for biruk

Question #45437

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?

what is the rang of feasible units of labor that determines second stage of production?

Expert's answer

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.

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.

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