Question

6. A manufacturer's total cost function is given by C =
13
+ 3x + 400, where is the number
4
of units produced. At what level of output will average cost be minimum? What is this
minimum​

Answer 1

Step-by-step explanation:

(a) Taking the first derivative of the total cost function wrt to quantity (q) gives the marginal cost function

MC=

dq

dc

=q

2

+2

(b) Average cost function is given by the total cost function divided by the number of units (q).

AC=

q

c

=

3

q

2

+2+

q

300

(c)To find the level output at the average cost is minimum we have to set

dq

d(AC)

=0

⇒q

3

=450

⇒q=

3

450