Answer to Question #240680 in Economics for Ashe

Question

$$The production function of a given firm Is given by Q =200sqrtLK and the. associated cost function is given by 2L + 5K = 1000 A. Calculate the level of labor and capital input at the optimum level of production B. Calculate the MRTSL, K and MRTS k, L c. What is the level of output at the least cost combination of labor and capital inputs?$$

Answer 1

$$\frac{\delta Q}{\delta K}=100\sqrt{\frac{L}{K}}-5\lambda$$

$$\frac{\delta Q}{\delta L}=100\sqrt{\frac{K}{L}}-2\lambda$$

$$\lambda=20\sqrt{\frac{L}{K}}$$

$$L=2.5K$$

$$K=100$$

$$L=250$$