Answer to Question #294362 in Microeconomics for job

Question

4. Assume that Q= (1/3)L³-10L -21L represents short run production function in which only labor is variable input. Then

a) Find the number of labor employed where TPL is maximum. 

b) Find the number of labor employed where APL is equal to MPL 

c) Find the number of labor employed when APL is maximum 

d) Find the number of labor employed when MPL is maximum 

e) Find stages of production 

Answer 1

Solution:

a.). TPL is maximum when MPL is equal to zero.

Derive MPL:

MPL = $\frac{\partial Q} {\partial L}$ = L² – 10 – 21

Set MPL to zero and derive quantity:

L² – 10 – 21 = 0

L = 5.57

The number of labor employed when TPL is maximum = 5.57 units

 

b.). APL = $\frac{Q} {L}$ = $\frac{\frac{1}{3} L^{3} -10L - 21L } {L} =$ $\frac{L^{2} }{3} - 10 - 21$

Set APL = MPL

$\frac{L^{2} }{3} - 10 - 21$ = L² – 10 – 21

L = 0

The number of labor employed when APL is equal to MPL = 0

 

c.). Set APL = 0

$\frac{L^{2} }{3} - 10 - 21 =0$

L = 9.6

The number of labor employed when APL is maximum = 9.6 units

 

d.). Set MPL to zero and derive quantity:

L² – 10 – 21 = 0

L = 5.57

The number of labor employed when MPL is maximum = 5.57 units

 

e.). The stages of production are: Increasing returns, decreasing but positive returns, and negative returns.