Question

The market demand function for a particular product is given by P=14-2q and the average cost AC=2q-2+4/q.
You are required to determine the output that
i. Minimizes average cost
ii. Maximizes revenue
III. Maximizes profit

Answer 1

i. The output that minimizes average cost is:

AC = min, if $AC'(q) = 0$ , so:

$2 - 4/q^2 = 0,$

q = 1.41 units.

ii. The output that maximizes revenue is:

TR = max, if $TR'(q) = 0$ , so:

14 - 4q = 0,

q = 3.5 units.

III. The output that maximizes profit is:

MR = MC, so:

14 - 4q = 4q - 2,

q = 2 units.