Question

i. Suppose that the production function for compact disc player is

𝑄=100𝐿0.6𝐾0.4

Where 𝑄 is the total output, 𝐿 is the quantity of labor employed, and 𝐾 is the quantity of capital in place.

a) Calculate TP, AP, and MP for the sixth, seventh and eighth units of labour employed if capital is fixed at 240 units.

Answer 1

Given 

$Q= 100L^{0.6}K^{0.4} ....... (1)$

Where Q is total output, L is the quantity of labor employed. K is quantity of capital. 

If capital is fixed at $K=240$

So 

$Q= 100L^{0.6} 240^{0.4}$

$Q= 895.54 L^{0.6} ...... (2)$

Average product of labor, 

Dividing output function by L

$AP(L) = 895.54 L^{(-0.4)} ....... (3)$

Marginal product of labor, differentiate equation 2 w r t L

$MP(L) =TP(n)-TP(n-1) .......... (4)$

 

When $L = 6$

$Q= 895.54{ (6^{0.6})}\\ Q= 2624.07$

So total product is$2624.07$

Average product 

$AP= 895.54 (6)^{(-0.4)}=437.345$

Marginal product of labor$MP(6) =Q(6)-Q(5) =2624.07-895.54 (5^{0.6}) =271.91$

When labor is L= 7 

Total product 

$Q= 895.54 (7^{0.6})\\ Q= 2878.35$

So total product is $2878.35$

Average product 

$AP= 895.54 (7)^{(-0.4)}=411.19$

Marginal product of labor

$MP(7) =TP(7)-TP(6) =254.28$

When L = 8

Total product 

$Q= 895.54 (8^{0.6}) \\ Q= 3118.45$

So total product is $3118.45$

Average product 

$AP= 895.54 (8)^{(-0.4)}=389.81$

Marginal product of labor

$MP(8) =TP(8)-TP(7)= 240.1$