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?

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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