A firm's production process uses labor, $L$, and capital, $K$, to produce an output, $Q$ according to the function $Q = 25 K L$. Let labor be fixed at level $L = L$. What is the cost minimizing level of capital that the firm must use to produce a target level of output, $Q = Q$ ?
A) $K = \frac { \bar { L } } { 25 Q }$
B) $K = 25 \bar { L } Q$
C) $K = \frac { \bar { Q } } { 25 \bar { L } }$
D) $K = \frac { Q ^ { 2 } } { 2500 \bar { L } }$

Question

Quizplus · Accepted Answer

Given the production function $Q = 25KL$, and with labor fixed at $L = \bar{L}$, to find the level of capital $K$ that produces a target output $Q = \bar{Q}$, we rearrange the equation to solve for $K$: $K = \frac{\bar{Q}}{25\bar{L}}$. This isolates $K$ as a function of the given $Q$ and fixed $L$, showing the relationship between capital required and the fixed labor to achieve a certain output level.

A Firm's Production Process Uses Labor LLL , and Capital KKK , to Produce an Output

A Firm's Production Process Uses Labor $L$ , and Capital $K$ , to Produce an Output