Suppose that a firm's production function can be specified as $Q = 10 K L$ Which of the following accurately describes this firm's long run total cost function?
A) $\frac { Q } { 10 K }$
B) $\frac { Q } { 10 L }$
C) $2 \sqrt { r w Q / 10 }$
D) $2 \sqrt { 10 Q / r w }$

Question

Suppose that a firm's production function can be specified as $Q = 10 K L$ Which of the following accurately describes this firm's long run total cost function? 
A) $\frac { Q } { 10 K }$
B) $\frac { Q } { 10 L }$
C) $2 \sqrt { r w Q / 10 }$
D) $2 \sqrt { 10 Q / r w }$

Quizplus · Accepted Answer

The correct answer is derived from the Cobb-Douglas production function $Q = 10KL$, where $K$ is capital and $L$ is labor. In the long run, firms can adjust both $K$ and $L$, and they will do so in a way that minimizes cost. The cost function in the long run can be derived using the concept of cost minimization, which involves the prices of the inputs (capital $r$ and labor $w$), and the production level $Q$. The form $2 \sqrt { r w Q / 10 }$ correctly represents the long-run total cost function for this production function, taking into account the prices of labor and capital and the quantity produced.

Suppose That a Firm's Production Function Can Be Specified As Q