Answer to Question #256531 in Microeconomics for Martina

Question

In the short run K is fixed at 16,000 hours. What is the short run demand for labor?

Answer 1

Margarita Robotics has a daily production function given by Q = K1⁄2 L1⁄2, where K is the monthly hours of use of 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.

In the short run, K is fixed at 16,000 hours. What is the short run demand for labor?

$Q=K^{1/2}L^{1/2}$

The short run demand for labor is

$Q=16000^{1/2}L^{1/2} \\ L^{1/2} = \frac{Q}{16000^{1/2}} \\ L = (\frac{Q}{16000^{1/2}})^2 \\ L= \frac{Q^2}{16000}$