Question

1.     A cob Douglas production function for a firm is given as Q=4L ½ K½. The firm has also established that wage rate and interest paid on capital are $3 and $5 respectively for a production period. The firm intents to spend $200 million for the period on production cost. Compute the levels of capital and labor that will maximize output. What is the maximum output?

Answer 1

$$\frac {\delta Q}{\delta L}=2(\frac{K}{L})^{0.5}$$

$$\frac {\delta Q}{\delta K}=2(\frac{L}{K})^{0.5}$$

$$3L+5K=200$$

$$L=0.6K$$

$$K=29$$

$$L=17$$