<p>Note first that the higher of the two lines is labelled demand as well as average revenue. In the case of demand it is natural to think of price determining quantity rather than quantity determining price. That there exists a least price at which quantity demanded is zero, and that that price is higher than any price at which quantity demanded is positive, makes perfect sense.  So there is no reason why the demand line should not extend to zero quantity.</p>
<p>The case of average revenue (<span class="math-container">$AR$</span>) is a bit more complicated.  Here it is more natural to think of the monetary amount as determined by the quantity sold (<span class="math-container">$QS$</span>). We have:</p>
<p><span class="math-container">$$AR=\dfrac{TR}{QS}$$</span></p>
<p>where <span class="math-container">$TR$</span> is total revenue. If <span class="math-container">$QS=0$</span> this reduces to zero divided by zero, which is not zero but <a href="https://en.wikipedia.org/wiki/Division_by_zero#:%7E:text=A%20positive%20or%20negative%20number,divided%20by%20zero%20is%20zero." rel="nofollow noreferrer">undefined</a>. Nevertheless, <em>provided total revenue is a suitable function of quantity sold</em> (a linear function for example as shown in the diagram in the question), average revenue at quantity zero can be defined as a limit:</p>
<p><span class="math-container">$$AR(QS=0) = \lim_{QS \to 0}\dfrac{TR(QS)}{QS}$$</span></p>
<p>Similar considerations apply to marginal revenue.</p>

CC BY-SA 4.0
2023-11-19T18:05:49.400Z
2023-11-19T18:05:49.400Z
Adam Bailey
<p>The following is from an exam question:</p>
<p><a href="https://i.sstatic.net/dGdBW.png" rel="nofollow noreferrer"><img src="https://i.sstatic.net/dGdBW.png" alt="an AR and MR diagram" /></a></p>
<p>To my mind this is plain nonsense. If Q is zero, AR and MR are zero, not some point above P1.</p>
<p>My question: is there any significance in drawing this diagram with lines extended all the way to zero on the x-axis? Why not just start at q=1 not q=0?</p>
<p>From the Mankiw textbook <a href="https://i.sstatic.net/tB4Oy.png" rel="nofollow noreferrer"><img src="https://i.sstatic.net/tB4Oy.png" alt="Monopoly Diagram" /></a>
we have the same approach, but this looks more deliberate, as cost lines <em>don't</em> claim to have values for q=0</p>
<p>In a sense it doesn't matter, but is it not just adding quite un-needed confusion?
What am I missing?</p>

<marginal>
MR Diagrams touching y axis
havlock
# MR Diagrams touching y axis

(Asked by: username_0 on 2023-11-19)

The following is from an exam question:

[![an AR and MR diagram](https://i.sstatic.net/dGdBW.png)](https://i.sstatic.net/dGdBW.png)

To my mind this is plain nonsense. If Q is zero, AR and MR are zero, not some point above P1.

My question: is there any significance in drawing this diagram with lines extended all the way to zero on the x-axis? Why not just start at q=1 not q=0?

From the Mankiw textbook [![Monopoly Diagram](https://i.sstatic.net/tB4Oy.png)](https://i.sstatic.net/tB4Oy.png)
we have the same approach, but this looks more deliberate, as cost lines *don't* claim to have values for q=0

In a sense it doesn't matter, but is it not just adding quite un-needed confusion?
What am I missing?

**Tags:** marginal


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## 1 answers

### Answer by username_1 on 2023-11-19. Score: 1 | Accepted answer

Note first that the higher of the two lines is labelled demand as well as average revenue. In the case of demand it is natural to think of price determining quantity rather than quantity determining price. That there exists a least price at which quantity demanded is zero, and that that price is higher than any price at which quantity demanded is positive, makes perfect sense. So there is no reason why the demand line should not extend to zero quantity.

The case of average revenue ($AR$) is a bit more complicated. Here it is more natural to think of the monetary amount as determined by the quantity sold ($QS$). We have:

$$AR=\dfrac{TR}{QS}$$

where $TR$ is total revenue. If $QS=0$ this reduces to zero divided by zero, which is not zero but [undefined](https://en.wikipedia.org/wiki/Division_by_zero#:%7E:text=A%20positive%20or%20negative%20number,divided%20by%20zero%20is%20zero.). Nevertheless, *provided total revenue is a suitable function of quantity sold* (a linear function for example as shown in the diagram in the question), average revenue at quantity zero can be defined as a limit:

$$AR(QS=0) = \lim\_{QS \to 0}\dfrac{TR(QS)}{QS}$$

Similar considerations apply to marginal revenue.


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