Question

suppose that the short run production function of shoe manufactured by certain ethiopian firm is given byq=4lsquare-0.2lcube where q reprsents the anual quantity of shoe quantity of shoe produced find AP of labour and MPof labour

Find the value of L that maxmize the out put

Find the value of L that maxmize marginal product

Find the valurle of L that maxmize averge product

Answer 1

AP of Labor and MP of Labor

$Q=4L^2-0.2L^3$

$AP(L)=\frac{Q}{L} =\frac{4L^2-0.2^3}{L}=4L-0.2L^2$

$MP(L)=\frac{\delta Q}{\delta L}= 8L-0.6L^2$

Value of L Maximizing Output

Here we take the value of MP and equate it to zero, and solve for L

$8L-0.6L^2=0$

$8L=0.6L^2$

$8=0.6L$

$\bold{L=13.33}$

Value of L that Maximize MP

Is taking the second derivative of the MP and equating it to zero.

$\frac{\delta MP}{\delta L}=8-1.2L$

$8-1.2L=0$

$\bold{L=6.67}$

Value of L that Maximizes Average Product

$MP=AP$

we find the derivative of AP and equate it to zero

$\frac{\delta AP}{\delta L} =4-0.4L=0$

$4=0.4L$

$\bold{L=10}$

At 10 units of labor, AP is maximized.