Question

Q = - 50 + 10 L – 0.02 L2

1) Find out MP

2) Find out AP

3) At what level of labor input does the AP curve reach its maximum? What is the MP at this input level?

Answer 1

Solution:

1.). MP =$\frac{\partial Q} {\partial L}$

Q = -50 + 10L – 0.02L²

MP = $\frac{\partial Q} {\partial L}$ = -0.04L + 10

MP = -0.04L + 10

 

2.). AP = $\frac{Q}{L}$

AP = -50 + 10L – 0.02L² $\div$ L = $-\frac{50}{L} -10 + 0.02L$

AP = $-\frac{50}{L} -10 + 0.02L$

 

3.). At maximum: AP = MP

$-\frac{50}{L} -10 + 0.02L$ = -0.04L + 10

$-\frac{50}{L} + 0.02L +0.04L$ = 10 + 10

$-\frac{50}{L} + 0.06L$ = 20

L = 335.81

AP curve reaches its maximum when labor = 335.81

 

MP = -0.04L + 10 = (-0.04 $\times$ 335.81) + 10 = -13.43 + 10 = -3.43

MP = -3.43