Question

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

Q = f(L) = 2.6667L0.75. The output price is $8 per unit and the wage is $5 per hour. Find the short-

run labor demand curve of the firm

Answer 1

Q = f(L) = 2.6667L^0.75

MRP_L = MR $\times$ MP_L = w

MR = P = 8

W = 5

MP_L = $\frac{\partial Q} {\partial L}$= 2.000025L^-0.25

MRP_L = 8 $\times$ 2.000025L^-0.25 = 16.0002L^-0.25

16.0002L^-0.25 = w

16.0002L^-0.25 = 5

$\frac{16.0002}{L^{0.25} }$ = 5

16.0002 = 5L^0.25

L = 104.86

The short-run labor demand curve of the firm = 104.86