Question

6. Cost Minimization Homework . Due in a day Practice Questions Convex Homework Unanswered Fill in the Blanks Suppose a firm with production function - LK faces input prices w1, 1, and wants to produce 100 units of output. If this firm is cost-minimizing, it will hire units of labor, units of capital, and will incura total cost of Unanswered 1 attempt left 7 Sub Fullscreen Show All X lecture7 (2).pdf lecture8.pdf lecture9.pdf

Answer 1

q = LK

Cost minimization condition is when MPL/MPK = w/r

MPL = K

MPK = L

w=1

r=1

So, MPL/MPK =w/r

K/L= 1/1

K =L

And q=100 units (given)

q= LK

So, 100 = L(L)

L² = 100

L = 10

K =10

wL+ rK = C

1(10) + (1)(10) = C

C =$ 20

Therefore, if this firm is cost-minimizing,it will hire 10 units of labor and 10 units of capital and will incur a total cost of $20.