I thought about possibility of occurring such event in the case of presence of fixed costs, but I would like to know others opinions.
closed as off-topic by Herr K., luchonacho, Giskard, Adam Bailey, jmbejara Oct 4 '17 at 0:23
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Yes, if there are non-zero fixed costs, and constant marginal cost, then average cost decreases strictly monotonically with quantity, asymptotic to the marginal cost.
Short answer: Yes, it is possible.
Decreasing average cost implies that marginal cost is less than average cost ($MC<AC$, which can be proved by simply taking the first derivative of $C(q)/q$). With constant marginal cost, there exists a simple linear cost function $C(q)=F+a\times q$ that satisfies the constant $MC$ condition, where the constant $F$ is the fixed cost and $a \times q$ is the variable cost, and the constant $a$ is $MC$. Therefore $AC=F/q+a$ is greater than $MC=a$.
Yes, but dropping fixed costs is not really a thing, is it? That is kind of the idea, you can't lower them easily