Question

• The short run production Q = L^3-2L^2-4L+40 determine the number labourers should be used to maximize production.

Answer 1

$Q = L^3 − 2L^2 − 4L + 40$

To determine the number of laborers that would maximize production, differentiate production function wrt to L

$\frac{∂Q}{∂L} = 3L^2 − 4L − 4$

Set this equal to

$\frac{∂Q}{∂L} = 3L^2 − 4L − 4=0$

$3L^2 + 2L - 6L - 4 = 0\\ (3L + 2)L - 2(3L + 2) = 0\\ (L − 2)\times(3L + 2) = 0$

$L^* = 2 \space and\space L^* = \frac{-2}{3}$

Since Labor cannot be negative, Hence L* = 2

Hence, L* = 2 maximises production.