Answer to Question #243550 in Economics for Ashenafi

Question

The production function of 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 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

A. The condition of optimum for producer is MP(L)/w=MP(K)/r (****); MP(L)=Q'(L)=1/2×200×L^(-1/2)×K^1/2; MP(K)=Q'(K)=1/2×200×L^1/2×K^(-1/2). w and r are prices for L and K, so they can be found from equation of costs: w= 2; r=5. Then, after simplification K=2/5 L. Applying this in the cost equation, 2L+5×2/5L=1000; L=250, K=100.

B)MRTS L,K =MP(L)/MP(K); Sipmlifying the relevant expressions from (A), we get

MRTS L K=K/L, MRTS K, L=L/K.

C) Q=200×sqrt(250×100)=31623