Question

Margarita Robotics has a daily production function given by Q= K 0.5 L 0.5, where K is the monthly of hours of use for a precision lathe (capital) and L is the monthly number of machinist hours (labor). Suppose that each unit of capital costs $40 and each unit of labor costs $10

Answer 1

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

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

$$r=40$$

$$w=10$$

$$\frac{L}{K}=4$$

$$L=4K$$