Question

The short run production function Q=L^3-2L^2-4L+40. determine the amount of laborers

Answer 1

$Q=L^3-2L^2-4L+40$

$\frac{\delta Q}{\delta L} =3L^2-4L-4$

Equate $\frac{\delta Q}{\delta L}=0$

$\implies$ $3L^2-4L-4=0$

Solving the above quadratic equation:

$L= \frac{4+(4^2-[4\times3\times-4])^\frac {1}{2}}{2\times3}$

$L=2$ labourers