Question

1. Consider the following production function: Q = f(K, L) = (K^1/2) (L^1/2)

a) Place capital on the vertical axis and labor on the horizontal axis. Determine the marginal rate of technical substitution.

b) Suppose that the price of capital is $10, 000, and the price of labor is $10, 000. What is the ratio of capital to labor that allows the firm to produce any given quantity of output as cheaply as possible.

c) Suppose that the price of capital increases to $30, 000. What is the ratio of capital to labor that allows the firm to produce any given quantity of output as cheaply as possible.

d) The price of capital is $10, 000, and the price of labor is $10, 000. Given this production technology determine the cost of producing 100 units of output, the average cost of producing 100 units, the capital to labor ratio, the factor demand for capital and the factor demand for labor.  

e)Suppose the price of capital increases to $40, 000. Determine the minimum cost of producing 100 units of output. What happens to the factor demands for capital and labor? If the factor demands change, explain why they change.

Answer 1

L 2 JL = mex = ১০ K 2JK MRTS 2 L MРК ST ZK MRTS PK=T= 10, 000 10,000 mininuiring At cost Cant MRTS L0 000 4or060

Pr=7= 30,000 PL=W= 10, 000 MRIS = 10,060 30,060 101000 MRTS L6000 L0060 KEL Prodn fh K SL put KEL L L=O Sin ce =100 K100 L =100 . Total cost wL+ 7Kk 1De000 00) + lo00o (I00) 000,000 + 1,000, o00 2,000, 00O

AC 21000, 0 AO AC 20000 el eK= T= NO W 4o,060 W = 101060 MRIS = 44660 L 4K iu prod 4K L put 2 20 = 50 O 100 2(1002 =200 WL+k p10,060 X 200 + 40,060 x50 2,000,050 2,000, 0ou +