Answer to Question #288539 in Microeconomics for fufu

Question

q=100kL. If the price of capital is r= $120 per day and the price of labor is w= $30 per day, What is the combination of labor and capital if the manufacturer wants to produce 100 units? 

Answer 1

For optimal combination, MRTS= the ratio of Wage rate to rental rate of capital

$MRTS= \frac{MP_L}{MP_K}=\frac{w}{r}$

$MP_L= \frac{\delta Q}{\delta L}= 100K$

$MP_K= \frac{\delta Q}{\delta K}= 100L$

$\frac{100K}{100L}=\frac{30}{120}\implies L=4K$

Substituting L in the cost production function

100=(100)(K)(4K)

$K^2=1\implies K=1$

L=4K$\implies$ L=4