<p>Based on the available information, you probably have to use the formula for point elasticity.</p>

CC BY-SA 4.0
2022-04-12T20:01:14.040Z
2022-04-12T20:01:14.040Z
Giskard
<p>Consider the demand function (i.e., your equation for the demand curve) <span class="math-container">$Q=D(p)$</span>. Then, the price elasticity of demand is
<span class="math-container">$$\varepsilon = \frac{\partial Q}{\partial p} \frac{p}{Q} = \frac{p D'(p)}{D(p)}$$</span></p>
<p>Suppose you know that at price <span class="math-container">$p_0$</span>, the quantity demanded <span class="math-container">$Q_0=D(p_0)$</span>. Then, the elasticity of demand at price <span class="math-container">$p_0$</span> is
<span class="math-container">$$\varepsilon = \frac{p_0 D'(p_0)}{D(p_0)}.$$</span></p>
<p><strong>Examples</strong></p>
<ol>
<li><p>Suppose <span class="math-container">$Q=D(p)=a - b \cdot p$</span>. Then, <span class="math-container">$$\varepsilon=-\frac{bp}{a - b \cdot p}$$</span>.</p>
</li>
<li><p>Suppose <span class="math-container">$Q=D(p)= a \cdot p^{-\epsilon}$</span>. Then, <span class="math-container">$D'(p) = -a\cdot\epsilon \cdot p^{-(\epsilon+1)}$</span>, and thus,</p>
</li>
</ol>
<p><span class="math-container">$$\varepsilon = \frac{p D'(p)}{D(p)} = -\frac{p \cdot a \cdot \epsilon \cdot p^{-(\epsilon+1)}}{a \cdot p^{-\epsilon}} = -\epsilon$$</span></p>

CC BY-SA 4.0
2022-05-13T02:05:10.790Z
2022-05-14T02:57:02.640Z
2022-05-14T02:57:02.640Z
Evangelos Con
<p>How does one calculate a firm's price elasticity of demand using the demand curve and only having the current price and the units sold per day?</p>

CC BY-SA 4.0
2022-04-12T14:48:06.503Z
Do you have an equation for the demand curve or just a single data point?
Giskard
CC BY-SA 4.0
2022-04-12T14:57:03.897Z
Hi, I have an equation for the demand curve
Anneke
<microeconomics>
Price elasticity of demand
Anneke
# Price elasticity of demand

(Asked by: username_0 on 2022-04-12)

How does one calculate a firm's price elasticity of demand using the demand curve and only having the current price and the units sold per day?

**Tags:** microeconomics
> **Comments:**
> **username_1**: Do you have an equation for the demand curve or just a single data point?  
> **username_0**: Hi, I have an equation for the demand curve  

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## 2 answers

### Answer by username_1 on 2022-04-12. Score: 1

Based on the available information, you probably have to use the formula for point elasticity.


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### Answer by username_2 on 2022-05-13. Score: 1

Consider the demand function (i.e., your equation for the demand curve) $Q=D(p)$. Then, the price elasticity of demand is
$$\varepsilon = \frac{\partial Q}{\partial p} \frac{p}{Q} = \frac{p D'(p)}{D(p)}$$

Suppose you know that at price $p\_0$, the quantity demanded $Q\_0=D(p\_0)$. Then, the elasticity of demand at price $p\_0$ is
$$\varepsilon = \frac{p\_0 D'(p\_0)}{D(p\_0)}.$$

**Examples**

1. Suppose $Q=D(p)=a - b \cdot p$. Then, $$\varepsilon=-\frac{bp}{a - b \cdot p}$$.
2. Suppose $Q=D(p)= a \cdot p^{-\epsilon}$. Then, $D'(p) = -a\cdot\epsilon \cdot p^{-(\epsilon+1)}$, and thus,

$$\varepsilon = \frac{p D'(p)}{D(p)} = -\frac{p \cdot a \cdot \epsilon \cdot p^{-(\epsilon+1)}}{a \cdot p^{-\epsilon}} = -\epsilon$$


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