A firm produces output that can be sold for 10 per unit The

A firm produces output that can be sold for $10 per unit. The production function is given by

Q = F (K, L) = K^½L^½

If K is fixed at I unit in the short run how much labor (L) should the firm employ to maximize profits if the wage rate is $2

Q = K^0.5L^0.5 = L^0.5 [Since short run K = 1]

Firm will employ labor upto the point when MRPL = w

Where MRPL = MPL x Price of output

MPL = dQ / dL = 0.5 / L^0.5

So,

0.5 / L^0.5 x $10 = $2

0.5 / L^0.5 = 2/10 = 0.2

L^0.5 = 0.5 / 0.2 = 2.5

L = (2.5)² = 6.25