Answer to Question #294119 in Microeconomics for job

Question

Assume that Q= (1/3)L³ -10L² -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

a)

$Q'=L^2-20L-21,$

$Q'=0,$

$TPL=21,$

b)

$APL=MPL=Q(21)=1764,$

c)

$Q=\frac{L^3}3-10L^2-21L,\\ Q=0,\\ APL=32,$

d)

$Q''=2L-20,$

$Q''=0,$

$L=10,$

$MPL=Q(10)=167.$