A perfectly competive firm has total revenue and total cost

A perfectly competive firm has total revenue and total cost curves given by:

TR=100Q

TC=5000 + 2Q + .02Q2

What is the average cost and at what point is it minimal?

Solution

Given , TC=5000 + 2Q + .02Q²

Average cost AC=TC/Q

AC=5000/Q+2+.02Q

to find the minimal point of the average cost, we need to differentiate AC.

dAC/dQ=-5000/Q² +.02

Average cost is minimum when dAC/dQ=0

5000/Q^{2 =}.02

250000=Q²

Q⁼500

Thus, average cost is minimum when Q=500 units.