<p>Honestly, you did a nice math, but in a wrong way, actually with a wrong base and pre assumption,
FC and VC, are quite different and get separate quantities and unrelated,
had it not been for TC, they would have never been relevant,
TC is resulted in summing up FC and VC..
FC is constant, let's assume its amount is Kf..
but VC will only be released by labour and capital ..L and K and the producted amount which is the same q,, not Kf.. let's say VC equals KL<em>q right now at this specific time, with this determined quantity for production.
and since TC gives Kf + KL</em>q
and MC is derivatives of TC based on the last added quantity(q), hence
MC = Kf + KL*q / q that concludes KL.
As the result, MC equals the amount of L and K which are quite variable and have being permanently changed..
MC, is never going to get a constant amount..
as MU doesn't etc.</p>

CC BY-SA 4.0
2024-09-16T20:10:59.183Z
2024-09-16T20:10:59.183Z
Yamir
<p>Your intuition is correct.</p>
<p>First, you're right that &quot;<em>marginal cost only depends on variable cost</em>&quot;, since
<span class="math-container">\begin{equation}
MC(q)=\frac{\mathrm dTC(q)}{\mathrm dq}=\frac{\mathrm d(FC+VC(q))}{\mathrm dq}=\frac{\mathrm dVC(q)}{\mathrm dq}. 
\end{equation}</span>
Next, if marginal cost is some constant <span class="math-container">$k$</span>, then variable cost must be <span class="math-container">$VC(q)=kq$</span>, because we can integrate <span class="math-container">$MC$</span> to obtain <span class="math-container">$TC$</span>, where the term that varies with <span class="math-container">$q$</span> is <span class="math-container">$kq$</span>:
<span class="math-container">\begin{equation}
MC(q)=k 
\quad\Rightarrow\quad 
\int k\;\mathrm dq =\underbrace{kq}_{VC(q)} +\underbrace{K\vphantom{q}}_{FC} 
\end{equation}</span>
where <span class="math-container">$K$</span> is a constant resulting from the integration.
Lastly,
<span class="math-container">\begin{equation}
AVC(q)=\frac{VC(q)}{q}=\frac{kq}{q}=k,
\end{equation}</span>
which is a constant, and same as <span class="math-container">$MC$</span>.</p>

CC BY-SA 4.0
2020-10-07T07:10:13.497Z
This is an *excellent* answer - thank you. One clarifying question: Sometimes in class our teacher will describe marginal cost as being "the cost of producing one additional unit." How does that relate to the calculus-based definition of marginal cost?
Will 
CC BY-SA 4.0
2020-10-07T15:06:31.817Z
If you look at the first derivative in the answer from @herr-k, notice that it's dTC/dq, which is the change in total cost w.r.t a one-unit change in quantity.  That's the definition your teacher gave.
Jeff
CC BY-SA 4.0
2020-10-07T15:16:14.680Z
@Will the cost of an extra unit is the discrete version of marginal costs and easier to understand as concept. For discrete production we can calculate the marginal cost only by determining what it costs to produce one additional unit. When quantity is continuous we can calculate the marginal cost at a point by calculating the cost of producing an infinitesimal extra unit.
Maarten Punt
CC BY-SA 4.0
2020-10-07T15:39:59.130Z
@Will: Thanks. In addition to the above two comments, you may also refer to [my answer](https://economics.stackexchange.com/a/9965/42) to a related question on this topic.
Herr K.
CC BY-SA 4.0
2020-10-07T04:20:20.307Z
2020-10-07T04:20:20.307Z
Herr K.
<p>I'm <em>inclined</em> to think yes because marginal cost only depends on variable cost (fixed costs don't matter), but I'm not 100% certain.</p>
<p>Basically, my thought process is that marginal cost of producing one additional unit is the change in total variable cost to produce that unit. So, my current idea is that if marginal cost is constant, that must mean that average variable cost (total variable cost/output) is also constant. But I'm still not entirely convinced.</p>

<microeconomics><cost><marginal><firm><theory-of-the-firm>
Is it true that if marginal cost is constant, then average variable cost is also constant and equals marginal cost?
Will 
# Is it true that if marginal cost is constant, then average variable cost is also constant and equals marginal cost?

(Asked by: username_0 on 2020-10-07)

I'm *inclined* to think yes because marginal cost only depends on variable cost (fixed costs don't matter), but I'm not 100% certain.

Basically, my thought process is that marginal cost of producing one additional unit is the change in total variable cost to produce that unit. So, my current idea is that if marginal cost is constant, that must mean that average variable cost (total variable cost/output) is also constant. But I'm still not entirely convinced.

**Tags:** microeconomics, cost, marginal, firm, theory-of-the-firm


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## 2 answers

### Answer by username_2 on 2020-10-07. Score: 6 | Accepted answer

Your intuition is correct.

First, you're right that "*marginal cost only depends on variable cost*", since
\begin{equation}
MC(q)=\frac{\mathrm dTC(q)}{\mathrm dq}=\frac{\mathrm d(FC+VC(q))}{\mathrm dq}=\frac{\mathrm dVC(q)}{\mathrm dq}.
\end{equation}
Next, if marginal cost is some constant $k$, then variable cost must be $VC(q)=kq$, because we can integrate $MC$ to obtain $TC$, where the term that varies with $q$ is $kq$:
\begin{equation}
MC(q)=k
\quad\Rightarrow\quad
\int k\;\mathrm dq =\underbrace{kq}\_{VC(q)} +\underbrace{K\vphantom{q}}\_{FC}
\end{equation}
where $K$ is a constant resulting from the integration.
Lastly,
\begin{equation}
AVC(q)=\frac{VC(q)}{q}=\frac{kq}{q}=k,
\end{equation}
which is a constant, and same as $MC$.

> **Comments:**
> **username_0**: This is an *excellent* answer - thank you. One clarifying question: Sometimes in class our teacher will describe marginal cost as being "the cost of producing one additional unit." How does that relate to the calculus-based definition of marginal cost?  
> **username_3**: If you look at the first derivative in the answer from @herr-k, notice that it's dTC/dq, which is the change in total cost w.r.t a one-unit change in quantity.  That's the definition your teacher gave.  
> **username_4**: @username_0the cost of an extra unit is the discrete version of marginal costs and easier to understand as concept. For discrete production we can calculate the marginal cost only by determining what it costs to produce one additional unit. When quantity is continuous we can calculate the marginal cost at a point by calculating the cost of producing an infinitesimal extra unit.  
> **username_2**: @Will: Thanks. In addition to the above two comments, you may also refer to [my answer](https://economics.stackexchange.com/a/9965/42) to a related question on this topic.  

---

### Answer by username_1 on 2024-09-16. Score: -1

Honestly, you did a nice math, but in a wrong way, actually with a wrong base and pre assumption,
FC and VC, are quite different and get separate quantities and unrelated,
had it not been for TC, they would have never been relevant,
TC is resulted in summing up FC and VC..
FC is constant, let's assume its amount is Kf..
but VC will only be released by labour and capital ..L and K and the producted amount which is the same q,, not Kf.. let's say VC equals KL*q right now at this specific time, with this determined quantity for production.
and since TC gives Kf + KL*q
and MC is derivatives of TC based on the last added quantity(q), hence
MC = Kf + KL\*q / q that concludes KL.
As the result, MC equals the amount of L and K which are quite variable and have being permanently changed..
MC, is never going to get a constant amount..
as MU doesn't etc.


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