Question

A firm has a cost function given by c(y) = 100y2 + 1000. At what output is average cost minimized?

Answer 1

Solution:-
There is a mistake in this question. The cost function must be 10y² + 1000 instead of 100y²+1000.
When Marginal Cost = Average Variable Cost, at that output the average cost is minimized.
MC = 20y, AVC = 10y + 1000/y
MC = AVC ⇒ 20y = 10y + 1000/y
⇒ 20y - 10y = 1000/y
⇒ 10y = 1000/y
⇒ 10y² = 1000
y² = 1000/10
y² = 100
y = √100
y = 10
Answer