<p>The answer will vary slightly depending on which notion of elasticity you're using. </p>

<p><a href="https://en.wikipedia.org/wiki/Arc_elasticity" rel="noreferrer"><strong>Arc elasticity</strong></a> (or <strong>midpoint</strong> elasticity) uses the formula
<span class="math-container">\begin{equation}
\epsilon^\text{arc}=\frac{Q_1-Q_0}{P_1-P_0}\cdot\frac{\frac12(Q_0+Q_1)}{\frac12(P_0+P_1)},
\end{equation}</span>
where <span class="math-container">$\frac12(Q_0+Q_1)$</span> is the midpoint between <span class="math-container">$Q_0$</span> and <span class="math-container">$Q_1$</span>. Note that in your case, <span class="math-container">$7.5$</span> is the midpoint between <span class="math-container">$7$</span> and <span class="math-container">$8$</span>. </p>

<p><a href="https://en.wikipedia.org/wiki/Elasticity_of_a_function" rel="noreferrer"><strong>Point elasticity</strong></a> uses the formula
<span class="math-container">\begin{equation}
\epsilon^\text{point}=\frac{\mathrm dQ}{\mathrm dP}\cdot\frac{P}{Q}.
\end{equation}</span>
Here, <span class="math-container">$\frac{\mathrm dQ}{\mathrm dP}$</span> is the derivative of the demand function (evaluated at the point you want to calculate the elasticity, but it will be constant if demand is linear), and in your case, <span class="math-container">$P=7.5$</span> and <span class="math-container">$Q$</span> is the quantity demanded corresponding to that price. </p>

CC BY-SA 4.0
2019-04-23T02:46:52.813Z
Thanks alot Herr. :) Corrected it . I'm having another small question. The PED value I received at price 7.5 is, 0.9641. Does it mean this is inelastic since it is smaller than 1. What Can I do to increase the revenue of the product. Increase or decrease the product
Hiru
CC BY-SA 4.0
2019-04-23T03:42:32.540Z
@Hiru: If you assume linear demand, then there is a nice property you can use. Suppose $Q^*$ is the quantity where $\epsilon=1$, then we must have $\epsilon >1$ for all $Q<Q^*$ and $\epsilon <1$ for all $Q>Q^*$.
Herr K.
CC BY-SA 4.0
2019-04-22T17:16:24.293Z
2019-04-22T17:16:24.293Z
Herr K.
<p>Hi I was given the following price vs quantity values.</p>

<pre><code>Price   Quantity Demanded
4   221
5   210
6   185
7   162
8   144
9   122
10  102
11  81
12  61
13  46
14  25
</code></pre>

<p>The graph was plotted as shown below.</p>

<p><a href="https://i.sstatic.net/8NqLH.png" rel="nofollow noreferrer"><img src="https://i.sstatic.net/8NqLH.png" alt="enter image description here"></a></p>

<p>The equation was, <span class="math-container">$Y = -0.0496 X + 15.133$</span>. What I need to know is, I was asked to find the PED when price is <span class="math-container">$\$7.5$</span>.</p>

<p>Then what I did was, I found the quantity at price <span class="math-container">$7.5$</span> substituting to the price quantity equation. And then found the PED using the equation</p>

<p><a href="https://i.sstatic.net/M4YQv.png" rel="nofollow noreferrer"><img src="https://i.sstatic.net/M4YQv.png" alt="enter image description here"></a></p>

<p>The quantity derived for price <span class="math-container">$7.5$</span> was <span class="math-container">$153.89$</span>. Then I calculated the PED as below. Is it correct?</p>

<p><span class="math-container">$$\frac{(153.89-144)/144}{(7.5-8)/8} = 1.099$$</span></p>

<p>May I know whether this calculation is correct?</p>

CC BY-SA 4.0
2019-04-22T16:51:12.417Z
Is Y = -0.0496 X + 15.133 your formula for quantity demanded?
Ali
<microeconomics><elasticity>
Calculating Price Elasticity of Demand
Hiru
# Calculating Price Elasticity of Demand

(Asked by: username_0 on 2019-04-22)

Hi I was given the following price vs quantity values.
Price   Quantity Demanded
4   221
5   210
6   185
7   162
8   144
9   122
10  102
11  81
12  61
13  46
14  25

The graph was plotted as shown below.

The equation was, $Y = -0.0496 X + 15.133$. What I need to know is, I was asked to find the PED when price is $\$7.5$.
Then what I did was, I found the quantity at price $7.5$ substituting to the price quantity equation. And then found the PED using the equation

The quantity derived for price $7.5$ was $153.89$. Then I calculated the PED as below. Is it correct?
$$\frac{(153.89-144)/144}{(7.5-8)/8} = 1.099$$
May I know whether this calculation is correct?

**Tags:** microeconomics, elasticity
> **Comments:**
> **username_1**: Is Y = -0.0496 X + 15.133 your formula for quantity demanded?  

---

## 1 answers

### Answer by username_2 on 2019-04-22. Score: 5 | Accepted answer

The answer will vary slightly depending on which notion of elasticity you're using.

[**Arc elasticity**](https://en.wikipedia.org/wiki/Arc_elasticity) (or **midpoint** elasticity) uses the formula
\begin{equation}
\epsilon^\text{arc}=\frac{Q\_1-Q\_0}{P\_1-P\_0}\cdot\frac{\frac12(Q\_0+Q\_1)}{\frac12(P\_0+P\_1)},
\end{equation}
where $\frac12(Q\_0+Q\_1)$ is the midpoint between $Q\_0$ and $Q\_1$. Note that in your case, $7.5$ is the midpoint between $7$ and $8$.

[**Point elasticity**](https://en.wikipedia.org/wiki/Elasticity_of_a_function) uses the formula
\begin{equation}
\epsilon^\text{point}=\frac{\mathrm dQ}{\mathrm dP}\cdot\frac{P}{Q}.
\end{equation}
Here, $\frac{\mathrm dQ}{\mathrm dP}$ is the derivative of the demand function (evaluated at the point you want to calculate the elasticity, but it will be constant if demand is linear), and in your case, $P=7.5$ and $Q$ is the quantity demanded corresponding to that price.

> **Comments:**
> **username_0**: Thanks alot Herr. :) Corrected it . I'm having another small question. The PED value I received at price 7.5 is, 0.9641. Does it mean this is inelastic since it is smaller than 1. What Can I do to increase the revenue of the product. Increase or decrease the product  
> **username_2**: @Hiru: If you assume linear demand, then there is a nice property you can use. Suppose $Q^*$ is the quantity where $\epsilon=1$, then we must have $\epsilon >1$ for all $Q<Q^*$ and $\epsilon <1$ for all $Q>Q^*$.  

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