Question

In the short run, a competitive firm has a production function,

Q = f(L) = 2.6667L0.75. The output price is $4 per unit and the wage is $5 per hour. Find the shortrun labor demand curve of the firm.

Answer 1

$Q= f(L)= 2.6667L^{0.75}$

Wage,w =5

Output price, p =4.

Labor demand curve, $L= f(w,p)$

$MP_L= \frac{\delta Q}{\delta L}=\alpha AL^{\alpha -1}$

$= 0.75\times2.6667\times L^{0.75-1}$

$=2L^{0.75-1}$

$MP_L= \frac{W}{P}$

$2L^{-0.25}=\frac{5}{4}$

$L=5.$

The short run labor demand will be 5.