Suppose that a firm uses both labor (L)and capital (K)as inputs.The firm's long-run production function is Q = F(L,K)= 8√L√K.The firm has _____ units of capital.If the firm uses an efficient production method and hires _____ workers,it can produce _____ units of output.
A) 100; 100; 1,200
B) 100; 225; 800
C) 225; 100; 1,200
D) 225; 225; 1,000

Question

Quizplus · Accepted Answer

To find out the amount of units of capital and workers needed to produce a certain amount of output, we need to use the production function Q=F(L,K)=8√L√K.

Let's first find out the units of capital needed to produce 1,200 units of output:

1,200 = 8√L√K

Divide both sides by 8:

150 = √L√K

Square both sides:

22,500 = LK

We know that the firm has 225 units of capital, so we can solve for the amount of workers needed:

22,500 = L(225)

L = 100

Therefore, the firm needs 100 workers to produce 1,200 units of output.

The best choice is C, which matches these values.

Suppose That a Firm Uses Both Labor (L)and Capital (K)as