# Is it possible to have constant marginal cost and decreasing average cost simultaneously? [closed]

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, jmbejaraOct 4 '17 at 0:23

This question appears to be off-topic. The users who voted to close gave this specific reason:

• "This question does not meet the standards for homework questions as spelled out in the relevant meta posts. For more information, see our policy on homework question and the general FAQ." – Herr K., luchonacho, Giskard, Adam Bailey, jmbejara

## 3 Answers

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

• I think either you or I have misunderstood the question. I don't see any mention of dropping fixed costs in the question. – EnergyNumbers Oct 2 '17 at 15:05
• That would likely be me. The average cost can only sink, when the cost function is variable C(x). Assuming C(x)= marginalcostx+fixed costs. Now if we want the marginal costs constant, .. I do see where I went wrong. I thought the term marginalx = const, but indeed the x is still variable. Still.. if we want dropping average costs, we need lower fixed costs to over compensate for the increasing marginal costs, which is not a thing. – Maurice Oct 2 '17 at 15:13
• @Maurice Average cost is equal to total cost, obvi, which consists of fixed cost and variable costs, since we have const mc it implies constant variable costs, but as quantity rises average fixed cost goes down, while avc stays the same. Hence, AC is decreasing at the same time of presence const mc – Alice Oct 2 '17 at 15:37