Question

1)     If the total production function given as: TP = 16L² - 0.4L³ then;

A)   Find the maximum value of APL and MPL.

Calculate the maximum production 

Answer 1

Given $TP=16L^2-0.4L^3$, we find the maximum value of APL and MPL as follows.

$1)$

$APL = \frac{TP}{L}$

$APL = \frac{( 16L^{2}-0.4L^{3})}{L}$

$APL = 16L -0.4L^{2}$

The maximum value of APL can be determined by setting $APL=0$

Therefore,

$16L -0.4L^{2}=0$

$16L = 0.4L^2\implies16=0.4L$

$L = 40$

The maximum value of APL is 40.

$2)$

The MPL is found by differentiating TP with respect to L.

$MPL=TP'=32L-1.2L^2$.

The maximum value of MPL is found by setting MPL=0

So,

$32L-1.2L^2=0\implies32=1.2L\implies L=26.6667$

Therefore, the maximum value of APL and MPL will be 40 and 26.6667 respectively.

$3)$

The Maximum production can be determined by substituting the maximum value of MPL of 26.6667 in the total production function as follows.

$TP = 16L^{2}-0.4L^{3}$

$TP = 16\times(26.6667)^2 - 0.4\times(26.6667)^3$

$TP = 3792.6$

The Maximum production will be 3792.6