Question

The production function for earthquake detectors​ (Q) is given as​ follows: Q​ = 4K​1/2L​1/2 where K is the amount of capital employed and L is the amount of labor employed. The price of​ capital, PK​, is​ $18 and the price of​ labor, PL​, is​ $2. Refer to Scenario 2. Suppose that you receive an order for 60 earthquake detectors. How much labor will you use to minimize the cost of 60 earthquake​ detectors?

Answer 1

Answer ; MC = 6

Step-by-step explanation:

Q = U√K √L

MRTS = MPL/MPK = U√K x 1/2√L

U√L x 1/2 √K = K/L

At optimum,

MRTSS = PL/PK

= K/L = 2/18 = 1/9

L= 9K

Q= U√K√L

60 =U√K √9K

60 = U x 3 x K

K=5

L=9 X 5 = 45

TL= wl + rk = PL x L+ PK x K

= 2L + 18K

= 2x Q²/16K + 18 x Q²/16L

Q²/8K+ 9Q²/8L

=Q²/8 x 5+ 9Q²/8x 45 =1/40 x 2Q²

MC= Q²/20 = 2Q/20 = Q/10 =60/10 = 6

MC = 6

Answer 2

k= 5 units

L = 45 units

Step-by-step explanation:

check the picture attached for full explanation and i hope it helps you