Question

When a firm uses K units of capital and L units of labor, it can produce Q units of output with the production function Q = K√L. Each unit of capital costs 20, and each unit of labor costs 25. The level of K is fixed at 5 units. Find the equation of the firm’s short-run total cost curve?

Answer 1

Answer:

$STC = 20K + 25L = 20*5 + 25*[\frac{Q^2}{25}] = 100 + Q^2$

Explanation:

We are given:

K units of capital and L units of labor.

•Each unit of capital cost = 20

• Each unit of labor cost =25

• Level K is fixed at 5 units

We are told production function Q = K√L

Using the production functions and the values given, we can get that Q=5√L.

To find Q, the amount of labor will be given as:

$L = \frac{Q^2}{25}$

Therefore, the Short run total cost function (STC) will be:

$20K + 25L = 20*5 + 25[\frac{Q^2}{25}] = 100 + Q^2$