Question

A firm has a production function given as Q(K,L) = K½, L½. Given that labour cost (L) = Ksh.4 and capital (K) costs Ksh. 12 and the firm has a budget of Ksh. 30000. Determine; the objective and the constraint functions, formulate the optimisation problem of the firm , find the amounts of K and L that a firm should employ to optimize output.

Answer 1

$$\frac {\delta Q}{\delta K}=\frac {L^{\frac {1}{2}}}{2 \times {K^{\frac{1}{2}}}}$$

$$\frac {\delta Q}{\delta L}=\frac {K^{\frac {1}{2}}}{2 \times {L^{\frac{1}{2}}}}$$

$$8L=24K$$

$$L=3K$$

$$4L+12K=30000$$

$$24K=30000$$

$$L=3750$$

$$K=1250$$