Question

A firm has the production function Q = KL, where K is the amount of capital and L is the amount of labor it uses as inputs. The cost per unit of capital is a rental fee r and the cost per unit of labor is a wage w. The conditional labor demand function L(Q, w, r) is

Answer 1

L(w,r,Q) = (Qr/w)*1/2

Step-by-step explanation:

The firm problem is to minimise l,k

W1,x1+ w2, x2

S.t.q= kl

The solution must satisfy mpl/ mpk= wl/wk and q=kl

From the first condition we get k/l= w/r

From which we can isolate k=lw/r

Then plug in k into the production function we find Q= (lw/r)(l) and isolating l

L(w,r,Q) = (Qr/w)*1/2

Attached is the written version of the solution