Question

The production function of given firm Is given by Q =200\sqrtLK  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 MRTS_L,_K and MRTS_k, _L

c. What is the level of output at the least cost combination of labor and capital inputs?

Answer 1

$$MU_K=100\sqrt{\frac{L}{K}}$$

$$MU_L=100\sqrt{\frac{K}{L}}$$

$$K=100$$

$$L=250$$

$$MRTS_{LK}=\frac{250}{100}=2.5$$

$$MRTS_{KL}=\frac{100}{250}=0.4$$

$$Q=100\sqrt{100\times250}=15811.4$$