<p>So using your above statements in the comments it should be relatively clear how to find that <span class="math-container">$MC = AVC$</span>. 
<span class="math-container">$$MC = \frac{\partial TC}{\partial Q} = 12$$</span>
and then using the fact that variable cost is <span class="math-container">$12Q$</span>
<span class="math-container">$$AVC = \frac{VC}{Q} = 12$$</span></p>

CC BY-SA 4.0
2019-11-03T10:19:02.507Z
From the maths I can see it works but could you explain the intuition behind it please?
Andrew Andreas
CC BY-SA 4.0
2019-11-03T17:25:04.740Z
Basically, given the functional form for the total cost function, you can see that neither of the above depend on $Q$. The marginal cost is constant and does not vary at different points. You can think of it in terms of the graph, if you were to plot your total cost function it would be an upward sloping line starting at 50 with a slope of 12. And if marginal cost is the derivative then it *is* the slope, which does not change. Same thing for average variable cost, it does not vary with $Q$. And this makes sense as the variable cost is $\$12$ per unit of $Q$, which does not change.
Brennan
CC BY-SA 4.0
2019-11-02T22:23:24.957Z
2019-11-02T22:23:24.957Z
Brennan
<p>If you are familiar with derivatives then the other answer is more appropriate. If you are not you can think of it this way : </p>

<p>(1) since the cost function is 50+ 12Q, whenever you produce 1 unit of the good your total cost is increased by twelve (Q1 -Q0). Therefore the marginal cost is 12.</p>

<p>(2) The AVC is calculated this way : VC / Q. Therefore AVQ = 12Q / Q = 12</p>

<ul>
<li>you can see that (1) and (2) give the same result so MC = AVC</li>
</ul>

CC BY-SA 4.0
2019-11-04T04:14:16.423Z
2019-11-04T04:14:16.423Z
alek racicot
<p>I was hoping someone could explain the following. Suppose the short-run total cost function is TC = 50 + 12Q. Which of the following statements is true at all levels of production?</p>

<p>The correct answer given was that MC = AVC</p>

<p>Could someone explain to me why please?</p>

CC BY-SA 4.0
2019-11-02T20:27:55.163Z
Do you know how to derive MC and AVC in general?
Herr K.
CC BY-SA 4.0
2019-11-02T22:10:24.513Z
MC = derivative of TC and AVC is TVC/Q?
Andrew Andreas
<microeconomics>
Why does average variable cost = marginal cost for this function?
Andrew Andreas
# Why does average variable cost = marginal cost for this function?

(Asked by: username_0 on 2019-11-02)

I was hoping someone could explain the following. Suppose the short-run total cost function is TC = 50 + 12Q. Which of the following statements is true at all levels of production?

The correct answer given was that MC = AVC

Could someone explain to me why please?

**Tags:** microeconomics
> **Comments:**
> **username_1**: Do you know how to derive MC and AVC in general?  
> **username_0**: MC = derivative of TC and AVC is TVC/Q?  

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## 2 answers

### Answer by username_2 on 2019-11-02. Score: 1 | Accepted answer

So using your above statements in the comments it should be relatively clear how to find that $MC = AVC$.
$$MC = \frac{\partial TC}{\partial Q} = 12$$
and then using the fact that variable cost is $12Q$
$$AVC = \frac{VC}{Q} = 12$$

> **Comments:**
> **username_0**: From the maths I can see it works but could you explain the intuition behind it please?  
> **username_2**: Basically, given the functional form for the total cost function, you can see that neither of the above depend on $Q$. The marginal cost is constant and does not vary at different points. You can think of it in terms of the graph, if you were to plot your total cost function it would be an upward sloping line starting at 50 with a slope of 12. And if marginal cost is the derivative then it *is* the slope, which does not change. Same thing for average variable cost, it does not vary with $Q$. And this makes sense as the variable cost is $\$12$ per unit of $Q$, which does not change.  

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### Answer by username_3 on 2019-11-04. Score: 0

If you are familiar with derivatives then the other answer is more appropriate. If you are not you can think of it this way :

(1) since the cost function is 50+ 12Q, whenever you produce 1 unit of the good your total cost is increased by twelve (Q1 -Q0). Therefore the marginal cost is 12.

(2) The AVC is calculated this way : VC / Q. Therefore AVQ = 12Q / Q = 12

* you can see that (1) and (2) give the same result so MC = AVC


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