Answer to Question #202504 in Microeconomics for Rida Awwal

Question

If TP = 8L2-0.2L3 based on this function;

A. Find the value of L that maximizes output

B. How many workers can maximize an extra production?

C. Calculate the value of labor that maximize APL

D. Find the maximum value of APL and MPL

E. Calculate the maximum production

Answer 1

(a)

Given in the question-

$TP = 8L^{2}-0.2L^{3}$  based on this function

Need to find-

Find the value of L that maximizes output

$\frac{\delta (TP)}{/\delta L} = \frac{\delta(8L^{2}-0.2L^{3} )}{\delta L}$

For, max. output 

$0 = 16L - 0.6L^{2}$

$16 = 0.6L$

$L = 27$

(b)

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

$APL = \frac{( 8L^{2}-0.2L^{3})}{L}$

$APL = 8L -0.2L^{2}$

(c)

For, Max. APL

$0 = 8L -0.2L^{2}$

$8 = 0.2L$

$L = 40$

(d)

Max value of APL will be "40" and Max. value of MPL will be "27"

(e)

Max. production will be

$TP = 8L^{2}-0.2L^{3}$

$TP = 8\times(27)^2 - 0.2\times(27)^3$

$TP = 1895.4$

Max. TP will be "1895.4"