Use the production function Q 4L12 K1 Suppose that the pric

Use the production function: Q = 4L1/2 K1 Suppose that the price of labor is $5 and the price of capital is $20. Your firm desires to produce 200 units of output. How much labor will be hired to minimize the costs of producing 200 units of output? A) 25 B) 50 C) 100 D) 200 E) none of the above 7. /2

Solution

Maximising profit

Profit (Pr)=P*Q-Cost

Pr=P*Q-5L-20K

Pr=P*4(LK)^0.5-4L-20K

dPr/dL=P*2(K/L)^0.5-4=0

dPr/dK=P*2(L/K)^0.5-20=0

We know equilibrium condition

MPL/MPK=w/r=5/20=0.25

MPL=2(K/L)^0.5 & MPK=2(L/K)^0.5

K/L=0.25

K=0.25L

200=4(0.25L^2)^0.5=4*0.5*L

L=100 units

Hence option C is correct answer